%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN068+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 08:07:07 PM UTC 2025 % Result : Theorem 3.62s 3.84s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYN068+1 : TPTP v9.2.0. Released v2.0.0. % 0.12/0.14 % Command : duper %s % 0.13/0.35 % Computer : n020.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 15:23:23 EDT 2025 % 0.20/0.35 % CPUTime : % 3.62/3.84 SZS status Theorem for theBenchmark.p % 3.62/3.84 SZS output start Proof for theBenchmark.p % 3.62/3.84 Clause #0 (by assumption #[]): Eq % 3.62/3.84 (∀ (X : Iota), % 3.62/3.84 big_f X → And (Exists fun Y => And (big_g Y) (big_h X Y)) (Exists fun Y1 => And (big_g Y1) (Not (big_h X Y1)))) % 3.62/3.84 True % 3.62/3.84 Clause #1 (by assumption #[]): Eq (Exists fun X => And (big_j X) (∀ (Y : Iota), big_g Y → big_h X Y)) True % 3.62/3.84 Clause #2 (by assumption #[]): Eq (Not (Exists fun X => And (big_j X) (Not (big_f X)))) True % 3.62/3.84 Clause #3 (by clausification #[2]): Eq (Exists fun X => And (big_j X) (Not (big_f X))) False % 3.62/3.84 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (And (big_j a) (Not (big_f a))) False % 3.62/3.84 Clause #5 (by clausification #[4]): ∀ (a : Iota), Or (Eq (big_j a) False) (Eq (Not (big_f a)) False) % 3.62/3.84 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (big_j a) False) (Eq (big_f a) True) % 3.62/3.84 Clause #7 (by clausification #[1]): ∀ (a : Iota), Eq (And (big_j (skS.0 0 a)) (∀ (Y : Iota), big_g Y → big_h (skS.0 0 a) Y)) True % 3.62/3.84 Clause #8 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (Y : Iota), big_g Y → big_h (skS.0 0 a) Y) True % 3.62/3.84 Clause #9 (by clausification #[7]): ∀ (a : Iota), Eq (big_j (skS.0 0 a)) True % 3.62/3.84 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (big_g a → big_h (skS.0 0 a_1) a) True % 3.62/3.84 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (big_g a) False) (Eq (big_h (skS.0 0 a_1) a) True) % 3.62/3.84 Clause #12 (by superposition #[9, 6]): ∀ (a : Iota), Or (Eq True False) (Eq (big_f (skS.0 0 a)) True) % 3.62/3.84 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (big_f (skS.0 0 a)) True % 3.62/3.84 Clause #14 (by clausification #[0]): ∀ (a : Iota), % 3.62/3.84 Eq (big_f a → And (Exists fun Y => And (big_g Y) (big_h a Y)) (Exists fun Y1 => And (big_g Y1) (Not (big_h a Y1)))) % 3.62/3.84 True % 3.62/3.84 Clause #15 (by clausification #[14]): ∀ (a : Iota), % 3.62/3.84 Or (Eq (big_f a) False) % 3.62/3.84 (Eq (And (Exists fun Y => And (big_g Y) (big_h a Y)) (Exists fun Y1 => And (big_g Y1) (Not (big_h a Y1)))) True) % 3.62/3.84 Clause #16 (by clausification #[15]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Exists fun Y1 => And (big_g Y1) (Not (big_h a Y1))) True) % 3.62/3.84 Clause #18 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (And (big_g (skS.0 1 a a_1)) (Not (big_h a (skS.0 1 a a_1)))) True) % 3.62/3.84 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (Not (big_h a (skS.0 1 a a_1))) True) % 3.62/3.84 Clause #20 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (big_g (skS.0 1 a a_1)) True) % 3.62/3.84 Clause #21 (by clausification #[19]): ∀ (a a_1 : Iota), Or (Eq (big_f a) False) (Eq (big_h a (skS.0 1 a a_1)) False) % 3.62/3.84 Clause #22 (by superposition #[21, 13]): ∀ (a a_1 : Iota), Or (Eq (big_h (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False) (Eq False True) % 3.62/3.84 Clause #28 (by superposition #[20, 13]): ∀ (a a_1 : Iota), Or (Eq (big_g (skS.0 1 (skS.0 0 a) a_1)) True) (Eq False True) % 3.62/3.84 Clause #31 (by clausification #[28]): ∀ (a a_1 : Iota), Eq (big_g (skS.0 1 (skS.0 0 a) a_1)) True % 3.62/3.84 Clause #32 (by superposition #[31, 11]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (big_h (skS.0 0 a) (skS.0 1 (skS.0 0 a_1) a_2)) True) % 3.62/3.84 Clause #33 (by clausification #[22]): ∀ (a a_1 : Iota), Eq (big_h (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) False % 3.62/3.84 Clause #36 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Eq (big_h (skS.0 0 a) (skS.0 1 (skS.0 0 a_1) a_2)) True % 3.62/3.84 Clause #37 (by superposition #[36, 33]): Eq True False % 3.62/3.84 Clause #38 (by clausification #[37]): False % 3.62/3.84 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------