%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN986+1.002 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 08:08:22 PM UTC 2025 % Result : Theorem 5.23s 5.43s % Output : Proof 5.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYN986+1.002 : TPTP v9.2.0. Released v4.0.0. % 0.11/0.13 % Command : duper %s % 0.14/0.35 % Computer : n022.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 15:46:38 EDT 2025 % 0.14/0.35 % CPUTime : % 5.23/5.43 SZS status Theorem for theBenchmark.p % 5.23/5.43 SZS output start Proof for theBenchmark.p % 5.23/5.43 Clause #0 (by assumption #[]): Eq (∀ (Y : Iota), r Y zero (succ Y)) True % 5.23/5.43 Clause #1 (by assumption #[]): Eq (∀ (Y X Z Z1 : Iota), r Y X Z → r Z X Z1 → r Y (succ X) Z1) True % 5.23/5.43 Clause #2 (by assumption #[]): Eq (Not (Exists fun Z2 => Exists fun Z1 => Exists fun Z0 => And (And (r zero zero Z2) (r zero Z2 Z1)) (r zero Z1 Z0))) % 5.23/5.43 True % 5.23/5.43 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r a zero (succ a)) True % 5.23/5.43 Clause #4 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (X Z Z1 : Iota), r a X Z → r Z X Z1 → r a (succ X) Z1) True % 5.23/5.43 Clause #5 (by clausification #[4]): ∀ (a a_1 : Iota), Eq (∀ (Z Z1 : Iota), r a a_1 Z → r Z a_1 Z1 → r a (succ a_1) Z1) True % 5.23/5.43 Clause #6 (by clausification #[5]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Z1 : Iota), r a a_1 a_2 → r a_2 a_1 Z1 → r a (succ a_1) Z1) True % 5.23/5.43 Clause #7 (by clausification #[6]): ∀ (a a_1 a_2 a_3 : Iota), Eq (r a a_1 a_2 → r a_2 a_1 a_3 → r a (succ a_1) a_3) True % 5.23/5.43 Clause #8 (by clausification #[7]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r a a_1 a_2) False) (Eq (r a_2 a_1 a_3 → r a (succ a_1) a_3) True) % 5.23/5.43 Clause #9 (by clausification #[8]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (r a a_1 a_2) False) (Or (Eq (r a_2 a_1 a_3) False) (Eq (r a (succ a_1) a_3) True)) % 5.23/5.43 Clause #10 (by superposition #[9, 3]): ∀ (a a_1 : Iota), Or (Eq (r (succ a) zero a_1) False) (Or (Eq (r a (succ zero) a_1) True) (Eq False True)) % 5.23/5.43 Clause #11 (by clausification #[10]): ∀ (a a_1 : Iota), Or (Eq (r (succ a) zero a_1) False) (Eq (r a (succ zero) a_1) True) % 5.23/5.43 Clause #12 (by superposition #[11, 3]): ∀ (a : Iota), Or (Eq (r a (succ zero) (succ (succ a))) True) (Eq False True) % 5.23/5.43 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (r a (succ zero) (succ (succ a))) True % 5.23/5.43 Clause #14 (by superposition #[13, 9]): ∀ (a a_1 : Iota), % 5.23/5.43 Or (Eq True False) (Or (Eq (r (succ (succ a)) (succ zero) a_1) False) (Eq (r a (succ (succ zero)) a_1) True)) % 5.23/5.43 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (r (succ (succ a)) (succ zero) a_1) False) (Eq (r a (succ (succ zero)) a_1) True) % 5.23/5.43 Clause #16 (by superposition #[15, 13]): ∀ (a : Iota), Or (Eq (r a (succ (succ zero)) (succ (succ (succ (succ a))))) True) (Eq False True) % 5.23/5.43 Clause #17 (by clausification #[2]): Eq (Exists fun Z2 => Exists fun Z1 => Exists fun Z0 => And (And (r zero zero Z2) (r zero Z2 Z1)) (r zero Z1 Z0)) False % 5.23/5.43 Clause #18 (by clausification #[17]): ∀ (a : Iota), Eq (Exists fun Z1 => Exists fun Z0 => And (And (r zero zero a) (r zero a Z1)) (r zero Z1 Z0)) False % 5.23/5.43 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), Eq (Exists fun Z0 => And (And (r zero zero a) (r zero a a_1)) (r zero a_1 Z0)) False % 5.23/5.43 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), Eq (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 a_2)) False % 5.23/5.43 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (r zero zero a) (r zero a a_1)) False) (Eq (r zero a_1 a_2) False) % 5.23/5.43 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (r zero a a_1) False) (Or (Eq (r zero zero a_2) False) (Eq (r zero a_2 a) False)) % 5.23/5.43 Clause #28 (by clausification #[16]): ∀ (a : Iota), Eq (r a (succ (succ zero)) (succ (succ (succ (succ a))))) True % 5.23/5.43 Clause #30 (by superposition #[28, 22]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (r zero zero a) False) (Eq (r zero a (succ (succ zero))) False)) % 5.23/5.43 Clause #36 (by clausification #[30]): ∀ (a : Iota), Or (Eq (r zero zero a) False) (Eq (r zero a (succ (succ zero))) False) % 5.23/5.43 Clause #37 (by superposition #[36, 3]): Or (Eq (r zero (succ zero) (succ (succ zero))) False) (Eq False True) % 5.23/5.43 Clause #38 (by clausification #[37]): Eq (r zero (succ zero) (succ (succ zero))) False % 5.23/5.43 Clause #39 (by superposition #[38, 13]): Eq False True % 5.23/5.43 Clause #40 (by clausification #[39]): False % 5.23/5.43 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------