%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN333+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:07:25 PM UTC 2025 % Result : Theorem 3.45s 3.64s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SYN333+1 : TPTP v9.2.0. Released v2.0.0. % 0.04/0.14 % Command : duper %s % 0.13/0.36 % Computer : n026.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Thu Oct 2 15:17:23 EDT 2025 % 0.13/0.36 % CPUTime : % 3.45/3.64 SZS status Theorem for theBenchmark.p % 3.45/3.64 SZS output start Proof for theBenchmark.p % 3.45/3.64 Clause #0 (by assumption #[]): Eq % 3.45/3.64 (Not % 3.45/3.64 (Exists fun X => % 3.45/3.64 Exists fun Y => % 3.45/3.64 ∀ (Z : Iota), % 3.45/3.64 big_f X Y → And (And (big_f Y Z) (big_f Z Z)) (And (big_f X Y) (big_g X Y) → And (big_g X Z) (big_g Z Z)))) % 3.45/3.64 True % 3.45/3.64 Clause #1 (by clausification #[0]): Eq % 3.45/3.64 (Exists fun X => % 3.45/3.64 Exists fun Y => % 3.45/3.64 ∀ (Z : Iota), % 3.45/3.64 big_f X Y → And (And (big_f Y Z) (big_f Z Z)) (And (big_f X Y) (big_g X Y) → And (big_g X Z) (big_g Z Z))) % 3.45/3.64 False % 3.45/3.64 Clause #2 (by clausification #[1]): ∀ (a : Iota), % 3.45/3.64 Eq % 3.45/3.64 (Exists fun Y => % 3.45/3.64 ∀ (Z : Iota), % 3.45/3.64 big_f a Y → And (And (big_f Y Z) (big_f Z Z)) (And (big_f a Y) (big_g a Y) → And (big_g a Z) (big_g Z Z))) % 3.45/3.64 False % 3.45/3.64 Clause #3 (by clausification #[2]): ∀ (a a_1 : Iota), % 3.45/3.64 Eq % 3.45/3.64 (∀ (Z : Iota), % 3.45/3.64 big_f a a_1 → And (And (big_f a_1 Z) (big_f Z Z)) (And (big_f a a_1) (big_g a a_1) → And (big_g a Z) (big_g Z Z))) % 3.45/3.64 False % 3.45/3.64 Clause #4 (by clausification #[3]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Eq % 3.45/3.64 (Not % 3.45/3.64 (big_f a a_1 → % 3.45/3.64 And (And (big_f a_1 (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) % 3.45/3.64 (And (big_f a a_1) (big_g a a_1) → % 3.45/3.64 And (big_g a (skS.0 0 a a_1 a_2)) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))))) % 3.45/3.64 True % 3.45/3.64 Clause #5 (by clausification #[4]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Eq % 3.45/3.64 (big_f a a_1 → % 3.45/3.64 And (And (big_f a_1 (skS.0 0 a a_1 a_2)) (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) % 3.45/3.64 (And (big_f a a_1) (big_g a a_1) → % 3.45/3.64 And (big_g a (skS.0 0 a a_1 a_2)) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)))) % 3.45/3.64 False % 3.45/3.64 Clause #6 (by clausification #[5]): ∀ (a a_1 : Iota), Eq (big_f a a_1) True % 3.45/3.64 Clause #7 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Eq % 3.45/3.64 (And (And (big_f a (skS.0 0 a_1 a a_2)) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2))) % 3.45/3.64 (And (big_f a_1 a) (big_g a_1 a) → % 3.45/3.64 And (big_g a_1 (skS.0 0 a_1 a a_2)) (big_g (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)))) % 3.45/3.64 False % 3.45/3.64 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq (And (big_f a (skS.0 0 a_1 a a_2)) (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2))) False) % 3.45/3.64 (Eq % 3.45/3.64 (And (big_f a_1 a) (big_g a_1 a) → % 3.45/3.64 And (big_g a_1 (skS.0 0 a_1 a a_2)) (big_g (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2))) % 3.45/3.64 False) % 3.45/3.64 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or % 3.45/3.64 (Eq % 3.45/3.64 (And (big_f a a_1) (big_g a a_1) → % 3.45/3.64 And (big_g a (skS.0 0 a a_1 a_2)) (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2))) % 3.45/3.64 False) % 3.45/3.64 (Or (Eq (big_f a_1 (skS.0 0 a a_1 a_2)) False) (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)) % 3.45/3.64 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq (big_f a (skS.0 0 a_1 a a_2)) False) % 3.45/3.64 (Or (Eq (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) False) (Eq (And (big_f a_1 a) (big_g a_1 a)) True)) % 3.45/3.64 Clause #11 (by clausification #[9]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq (big_f a (skS.0 0 a_1 a a_2)) False) % 3.45/3.64 (Or (Eq (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) False) % 3.45/3.64 (Eq (And (big_g a_1 (skS.0 0 a_1 a a_2)) (big_g (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2))) False)) % 3.45/3.64 Clause #12 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq (big_f a (skS.0 0 a_1 a a_2)) False) % 3.45/3.64 (Or (Eq (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) False) (Eq (big_g a_1 a) True)) % 3.45/3.64 Clause #14 (by forward demodulation #[12, 6]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq True False) (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) (Eq (big_g a a_1) True)) % 3.45/3.64 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) (Eq (big_g a a_1) True) % 3.45/3.64 Clause #16 (by superposition #[15, 6]): ∀ (a a_1 : Iota), Or (Eq (big_g a a_1) True) (Eq False True) % 3.45/3.64 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (big_g a a_1) True % 3.45/3.64 Clause #21 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq (big_f a (skS.0 0 a_1 a a_2)) False) % 3.45/3.64 (Or (Eq (big_f (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) False) % 3.45/3.64 (Or (Eq (big_g a_1 (skS.0 0 a_1 a a_2)) False) (Eq (big_g (skS.0 0 a_1 a a_2) (skS.0 0 a_1 a a_2)) False))) % 3.45/3.64 Clause #22 (by forward demodulation #[21, 6]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq True False) % 3.45/3.64 (Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 3.45/3.64 (Or (Eq (big_g a (skS.0 0 a a_1 a_2)) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False))) % 3.45/3.64 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq (big_f (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 3.45/3.64 (Or (Eq (big_g a (skS.0 0 a a_1 a_2)) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)) % 3.45/3.64 Clause #24 (by forward demodulation #[23, 6]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq True False) % 3.45/3.64 (Or (Eq (big_g a (skS.0 0 a a_1 a_2)) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False)) % 3.45/3.64 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), % 3.45/3.64 Or (Eq (big_g a (skS.0 0 a a_1 a_2)) False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 3.45/3.64 Clause #26 (by forward demodulation #[25, 17]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False) % 3.45/3.64 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Eq (big_g (skS.0 0 a a_1 a_2) (skS.0 0 a a_1 a_2)) False % 3.45/3.64 Clause #28 (by superposition #[27, 17]): Eq False True % 3.45/3.64 Clause #29 (by clausification #[28]): False % 3.45/3.64 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------