%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN069+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n021.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 08:07:07 PM UTC 2025 % Result : Theorem 4.22s 4.40s % Output : Proof 4.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYN069+1 : TPTP v9.2.0. Released v2.0.0. % 0.08/0.14 % Command : duper %s % 0.13/0.34 % Computer : n021.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 15:16:23 EDT 2025 % 0.13/0.35 % CPUTime : % 4.22/4.40 SZS status Theorem for theBenchmark.p % 4.22/4.40 SZS output start Proof for theBenchmark.p % 4.22/4.40 Clause #0 (by assumption #[]): Eq % 4.22/4.40 (∀ (X : Iota), % 4.22/4.40 And (big_f X) (∀ (Y : Iota), And (big_g Y) (big_h X Y) → big_j X Y) → % 4.22/4.40 ∀ (Y1 : Iota), And (And (big_g Y1) (big_h X Y1)) (big_k Y1)) % 4.22/4.40 True % 4.22/4.40 Clause #1 (by assumption #[]): Eq (Not (Exists fun Y => And (big_l Y) (big_k Y))) True % 4.22/4.40 Clause #2 (by assumption #[]): Eq % 4.22/4.40 (Exists fun X => % 4.22/4.40 And (And (big_f X) (∀ (Y : Iota), big_h X Y → big_l Y)) (∀ (Y1 : Iota), And (big_g Y1) (big_h X Y1) → big_j X Y1)) % 4.22/4.40 True % 4.22/4.40 Clause #3 (by assumption #[]): Eq (Not (Exists fun X => And (big_f X) (Not (Exists fun Y => And (big_g Y) (big_h X Y))))) True % 4.22/4.40 Clause #4 (by clausification #[1]): Eq (Exists fun Y => And (big_l Y) (big_k Y)) False % 4.22/4.40 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (And (big_l a) (big_k a)) False % 4.22/4.40 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (big_l a) False) (Eq (big_k a) False) % 4.22/4.40 Clause #7 (by clausification #[0]): ∀ (a : Iota), % 4.22/4.40 Eq % 4.22/4.40 (And (big_f a) (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y) → % 4.22/4.40 ∀ (Y1 : Iota), And (And (big_g Y1) (big_h a Y1)) (big_k Y1)) % 4.22/4.40 True % 4.22/4.40 Clause #8 (by clausification #[7]): ∀ (a : Iota), % 4.22/4.40 Or (Eq (And (big_f a) (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y)) False) % 4.22/4.40 (Eq (∀ (Y1 : Iota), And (And (big_g Y1) (big_h a Y1)) (big_k Y1)) True) % 4.22/4.40 Clause #9 (by clausification #[8]): ∀ (a : Iota), % 4.22/4.40 Or (Eq (∀ (Y1 : Iota), And (And (big_g Y1) (big_h a Y1)) (big_k Y1)) True) % 4.22/4.40 (Or (Eq (big_f a) False) (Eq (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y) False)) % 4.22/4.40 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.22/4.40 Or (Eq (big_f a) False) % 4.22/4.40 (Or (Eq (∀ (Y : Iota), And (big_g Y) (big_h a Y) → big_j a Y) False) % 4.22/4.40 (Eq (And (And (big_g a_1) (big_h a a_1)) (big_k a_1)) True)) % 4.22/4.40 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota), % 4.22/4.40 Or (Eq (big_f a) False) % 4.22/4.40 (Or (Eq (And (And (big_g a_1) (big_h a a_1)) (big_k a_1)) True) % 4.22/4.40 (Eq (Not (And (big_g (skS.0 0 a a_2)) (big_h a (skS.0 0 a a_2)) → big_j a (skS.0 0 a a_2))) True)) % 4.22/4.40 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), % 4.22/4.40 Or (Eq (big_f a) False) % 4.22/4.40 (Or (Eq (Not (And (big_g (skS.0 0 a a_1)) (big_h a (skS.0 0 a a_1)) → big_j a (skS.0 0 a a_1))) True) % 4.22/4.40 (Eq (big_k a_2) True)) % 4.22/4.40 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), % 4.22/4.40 Or (Eq (big_f a) False) % 4.22/4.40 (Or (Eq (big_k a_1) True) % 4.22/4.40 (Eq (And (big_g (skS.0 0 a a_2)) (big_h a (skS.0 0 a a_2)) → big_j a (skS.0 0 a a_2)) False)) % 4.22/4.40 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), % 4.22/4.40 Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (And (big_g (skS.0 0 a a_2)) (big_h a (skS.0 0 a a_2))) True)) % 4.22/4.40 Clause #16 (by clausification #[14]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (big_j a (skS.0 0 a a_2)) False)) % 4.22/4.40 Clause #17 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (big_h a (skS.0 0 a a_2)) True)) % 4.22/4.40 Clause #18 (by clausification #[15]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_f a) False) (Or (Eq (big_k a_1) True) (Eq (big_g (skS.0 0 a a_2)) True)) % 4.22/4.40 Clause #19 (by clausification #[2]): ∀ (a : Iota), % 4.22/4.40 Eq % 4.22/4.40 (And (And (big_f (skS.0 1 a)) (∀ (Y : Iota), big_h (skS.0 1 a) Y → big_l Y)) % 4.22/4.40 (∀ (Y1 : Iota), And (big_g Y1) (big_h (skS.0 1 a) Y1) → big_j (skS.0 1 a) Y1)) % 4.22/4.40 True % 4.22/4.40 Clause #20 (by clausification #[19]): ∀ (a : Iota), Eq (∀ (Y1 : Iota), And (big_g Y1) (big_h (skS.0 1 a) Y1) → big_j (skS.0 1 a) Y1) True % 4.22/4.40 Clause #21 (by clausification #[19]): ∀ (a : Iota), Eq (And (big_f (skS.0 1 a)) (∀ (Y : Iota), big_h (skS.0 1 a) Y → big_l Y)) True % 4.22/4.40 Clause #22 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (And (big_g a) (big_h (skS.0 1 a_1) a) → big_j (skS.0 1 a_1) a) True % 4.22/4.40 Clause #23 (by clausification #[22]): ∀ (a a_1 : Iota), Or (Eq (And (big_g a) (big_h (skS.0 1 a_1) a)) False) (Eq (big_j (skS.0 1 a_1) a) True) % 4.22/4.40 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Or (Eq (big_j (skS.0 1 a) a_1) True) (Or (Eq (big_g a_1) False) (Eq (big_h (skS.0 1 a) a_1) False)) % 4.25/4.42 Clause #25 (by clausification #[21]): ∀ (a : Iota), Eq (∀ (Y : Iota), big_h (skS.0 1 a) Y → big_l Y) True % 4.25/4.42 Clause #26 (by clausification #[21]): ∀ (a : Iota), Eq (big_f (skS.0 1 a)) True % 4.25/4.42 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 1 a) a_1 → big_l a_1) True % 4.25/4.42 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (big_h (skS.0 1 a) a_1) False) (Eq (big_l a_1) True) % 4.25/4.42 Clause #29 (by clausification #[3]): Eq (Exists fun X => And (big_f X) (Not (Exists fun Y => And (big_g Y) (big_h X Y)))) False % 4.25/4.42 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (And (big_f a) (Not (Exists fun Y => And (big_g Y) (big_h a Y)))) False % 4.25/4.42 Clause #31 (by clausification #[30]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Not (Exists fun Y => And (big_g Y) (big_h a Y))) False) % 4.25/4.42 Clause #32 (by clausification #[31]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Exists fun Y => And (big_g Y) (big_h a Y)) True) % 4.25/4.42 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (And (big_g (skS.0 2 a a_1)) (big_h a (skS.0 2 a a_1))) True) % 4.25/4.42 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (big_h a (skS.0 2 a a_1)) True) % 4.25/4.42 Clause #36 (by superposition #[26, 17]): ∀ (a a_1 a_2 : Iota), % 4.25/4.42 Or (Eq True False) (Or (Eq (big_k a) True) (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True)) % 4.25/4.42 Clause #37 (by superposition #[26, 18]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (big_k a) True) (Eq (big_g (skS.0 0 (skS.0 1 a_1) a_2)) True)) % 4.25/4.42 Clause #38 (by superposition #[26, 34]): ∀ (a a_1 : Iota), Or (Eq (big_h (skS.0 1 a) (skS.0 2 (skS.0 1 a) a_1)) True) (Eq False True) % 4.25/4.42 Clause #40 (by superposition #[16, 26]): ∀ (a a_1 a_2 : Iota), % 4.25/4.42 Or (Eq True False) (Or (Eq (big_k a) True) (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) False)) % 4.25/4.42 Clause #43 (by clausification #[37]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_g (skS.0 0 (skS.0 1 a_1) a_2)) True) % 4.25/4.42 Clause #44 (by superposition #[43, 24]): ∀ (a a_1 a_2 a_3 : Iota), % 4.25/4.42 Or (Eq (big_k a) True) % 4.25/4.42 (Or (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) True) % 4.25/4.42 (Or (Eq True False) (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) False))) % 4.25/4.42 Clause #62 (by clausification #[36]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True) % 4.25/4.42 Clause #74 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 1 a) (skS.0 2 (skS.0 1 a) a_1)) True % 4.25/4.42 Clause #75 (by superposition #[74, 28]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_l (skS.0 2 (skS.0 1 a) a_1)) True) % 4.25/4.42 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (big_l (skS.0 2 (skS.0 1 a) a_1)) True % 4.25/4.42 Clause #77 (by superposition #[76, 6]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (big_k (skS.0 2 (skS.0 1 a) a_1)) False) % 4.25/4.42 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota), Eq (big_k (skS.0 2 (skS.0 1 a) a_1)) False % 4.25/4.42 Clause #80 (by superposition #[78, 62]): ∀ (a a_1 : Iota), Or (Eq False True) (Eq (big_h (skS.0 1 a) (skS.0 0 (skS.0 1 a) a_1)) True) % 4.25/4.42 Clause #87 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) False) % 4.25/4.42 Clause #91 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 1 a) (skS.0 0 (skS.0 1 a) a_1)) True % 4.25/4.42 Clause #100 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 4.25/4.42 Or (Eq (big_k a) True) % 4.25/4.42 (Or (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) True) % 4.25/4.42 (Eq (big_h (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_2) a_3)) False)) % 4.25/4.42 Clause #101 (by superposition #[100, 91]): ∀ (a a_1 a_2 : Iota), % 4.25/4.42 Or (Eq (big_k a) True) (Or (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True) (Eq False True)) % 4.25/4.42 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), Or (Eq (big_k a) True) (Eq (big_j (skS.0 1 a_1) (skS.0 0 (skS.0 1 a_1) a_2)) True) % 4.25/4.42 Clause #104 (by superposition #[102, 87]): ∀ (a a_1 : Iota), Or (Eq (big_k a) True) (Or (Eq (big_k a_1) True) (Eq True False)) % 4.25/4.42 Clause #111 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (big_k a) True) (Eq (big_k a_1) True) % 4.25/4.43 Clause #112 (by superposition #[111, 78]): ∀ (a : Iota), Or (Eq (big_k a) True) (Eq True False) % 4.25/4.43 Clause #116 (by clausification #[112]): ∀ (a : Iota), Eq (big_k a) True % 4.25/4.43 Clause #117 (by superposition #[116, 78]): Eq True False % 4.25/4.43 Clause #119 (by clausification #[117]): False % 4.25/4.43 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------