%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN327+1 : TPTP v9.2.0. Released v2.0.0. % 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 08:07:24 PM UTC 2025 % Result : Theorem 3.62s 3.82s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN327+1 : TPTP v9.2.0. Released v2.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Thu Oct 2 15:43:23 EDT 2025 % 0.13/0.35 % CPUTime : % 3.62/3.82 SZS status Theorem for theBenchmark.p % 3.62/3.82 SZS output start Proof for theBenchmark.p % 3.62/3.82 Clause #0 (by assumption #[]): Eq % 3.62/3.82 (Not % 3.62/3.82 (∀ (X : Iota), % 3.62/3.82 Exists fun Y => % 3.62/3.82 ∀ (Z : Iota), % 3.62/3.82 big_f Y X → And (big_f X Z → big_f X Y) (big_f X Y → Not (big_f X Z) → And (big_f Y X) (big_f Z Y)))) % 3.62/3.82 True % 3.62/3.82 Clause #1 (by clausification #[0]): Eq % 3.62/3.82 (∀ (X : Iota), % 3.62/3.82 Exists fun Y => % 3.62/3.82 ∀ (Z : Iota), big_f Y X → And (big_f X Z → big_f X Y) (big_f X Y → Not (big_f X Z) → And (big_f Y X) (big_f Z Y))) % 3.62/3.82 False % 3.62/3.82 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.62/3.82 Eq % 3.62/3.82 (Not % 3.62/3.82 (Exists fun Y => % 3.62/3.82 ∀ (Z : Iota), % 3.62/3.82 big_f Y (skS.0 0 a) → % 3.62/3.82 And (big_f (skS.0 0 a) Z → big_f (skS.0 0 a) Y) % 3.62/3.82 (big_f (skS.0 0 a) Y → Not (big_f (skS.0 0 a) Z) → And (big_f Y (skS.0 0 a)) (big_f Z Y)))) % 3.62/3.82 True % 3.62/3.82 Clause #3 (by clausification #[2]): ∀ (a : Iota), % 3.62/3.82 Eq % 3.62/3.82 (Exists fun Y => % 3.62/3.82 ∀ (Z : Iota), % 3.62/3.82 big_f Y (skS.0 0 a) → % 3.62/3.82 And (big_f (skS.0 0 a) Z → big_f (skS.0 0 a) Y) % 3.62/3.82 (big_f (skS.0 0 a) Y → Not (big_f (skS.0 0 a) Z) → And (big_f Y (skS.0 0 a)) (big_f Z Y))) % 3.62/3.82 False % 3.62/3.82 Clause #4 (by clausification #[3]): ∀ (a a_1 : Iota), % 3.62/3.82 Eq % 3.62/3.82 (∀ (Z : Iota), % 3.62/3.82 big_f a (skS.0 0 a_1) → % 3.62/3.82 And (big_f (skS.0 0 a_1) Z → big_f (skS.0 0 a_1) a) % 3.62/3.82 (big_f (skS.0 0 a_1) a → Not (big_f (skS.0 0 a_1) Z) → And (big_f a (skS.0 0 a_1)) (big_f Z a))) % 3.62/3.82 False % 3.62/3.82 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Eq % 3.62/3.82 (Not % 3.62/3.82 (big_f a (skS.0 0 a_1) → % 3.62/3.82 And (big_f (skS.0 0 a_1) (skS.0 1 a a_1 a_2) → big_f (skS.0 0 a_1) a) % 3.62/3.82 (big_f (skS.0 0 a_1) a → % 3.62/3.82 Not (big_f (skS.0 0 a_1) (skS.0 1 a a_1 a_2)) → And (big_f a (skS.0 0 a_1)) (big_f (skS.0 1 a a_1 a_2) a)))) % 3.62/3.82 True % 3.62/3.82 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Eq % 3.62/3.82 (big_f a (skS.0 0 a_1) → % 3.62/3.82 And (big_f (skS.0 0 a_1) (skS.0 1 a a_1 a_2) → big_f (skS.0 0 a_1) a) % 3.62/3.82 (big_f (skS.0 0 a_1) a → % 3.62/3.82 Not (big_f (skS.0 0 a_1) (skS.0 1 a a_1 a_2)) → And (big_f a (skS.0 0 a_1)) (big_f (skS.0 1 a a_1 a_2) a))) % 3.62/3.82 False % 3.62/3.82 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (big_f a (skS.0 0 a_1)) True % 3.62/3.82 Clause #8 (by clausification #[6]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Eq % 3.62/3.82 (And (big_f (skS.0 0 a) (skS.0 1 a_1 a a_2) → big_f (skS.0 0 a) a_1) % 3.62/3.82 (big_f (skS.0 0 a) a_1 → % 3.62/3.82 Not (big_f (skS.0 0 a) (skS.0 1 a_1 a a_2)) → And (big_f a_1 (skS.0 0 a)) (big_f (skS.0 1 a_1 a a_2) a_1))) % 3.62/3.82 False % 3.62/3.82 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Or (Eq (big_f (skS.0 0 a) (skS.0 1 a_1 a a_2) → big_f (skS.0 0 a) a_1) False) % 3.62/3.82 (Eq % 3.62/3.82 (big_f (skS.0 0 a) a_1 → % 3.62/3.82 Not (big_f (skS.0 0 a) (skS.0 1 a_1 a a_2)) → And (big_f a_1 (skS.0 0 a)) (big_f (skS.0 1 a_1 a a_2) a_1)) % 3.62/3.82 False) % 3.62/3.82 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Or % 3.62/3.82 (Eq % 3.62/3.82 (big_f (skS.0 0 a) a_1 → % 3.62/3.82 Not (big_f (skS.0 0 a) (skS.0 1 a_1 a a_2)) → And (big_f a_1 (skS.0 0 a)) (big_f (skS.0 1 a_1 a a_2) a_1)) % 3.62/3.82 False) % 3.62/3.82 (Eq (big_f (skS.0 0 a) a_1) False) % 3.62/3.82 Clause #15 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Or (Eq (big_f (skS.0 0 a) a_1) False) % 3.62/3.82 (Eq (Not (big_f (skS.0 0 a) (skS.0 1 a_1 a a_2)) → And (big_f a_1 (skS.0 0 a)) (big_f (skS.0 1 a_1 a a_2) a_1)) % 3.62/3.82 False) % 3.62/3.82 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (And (big_f a_1 (skS.0 0 a)) (big_f (skS.0 1 a_1 a a_2) a_1)) False) % 3.62/3.82 Clause #27 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Or (Eq (big_f (skS.0 0 a) a_1) False) % 3.62/3.82 (Or (Eq (big_f a_1 (skS.0 0 a)) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) False)) % 3.62/3.82 Clause #28 (by forward demodulation #[27, 7]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 Or (Eq (big_f (skS.0 0 a) a_1) False) (Or (Eq True False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) False)) % 3.62/3.82 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a) a_1) False) (Eq (big_f (skS.0 1 a_1 a a_2) a_1) False) % 3.62/3.82 Clause #31 (by superposition #[29, 7]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 1 (skS.0 0 a) a_1 a_2) (skS.0 0 a)) False) (Eq False True) % 3.62/3.82 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (big_f (skS.0 1 (skS.0 0 a) a_1 a_2) (skS.0 0 a)) False % 3.62/3.82 Clause #33 (by superposition #[32, 7]): Eq False True % 3.62/3.82 Clause #34 (by clausification #[33]): False % 3.62/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------