%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN986+1.001 : TPTP v9.2.0. Released v4.0.0. % 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 08:08:22 PM UTC 2025 % Result : Theorem 3.68s 3.85s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN986+1.001 : TPTP v9.2.0. Released v4.0.0. % 0.12/0.13 % Command : duper %s % 0.14/0.34 % Computer : n021.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 15:26:08 EDT 2025 % 0.14/0.34 % CPUTime : % 3.68/3.85 SZS status Theorem for theBenchmark.p % 3.68/3.85 SZS output start Proof for theBenchmark.p % 3.68/3.85 Clause #0 (by assumption #[]): Eq (∀ (Y : Iota), r Y zero (succ Y)) True % 3.68/3.85 Clause #1 (by assumption #[]): Eq (∀ (Y X Z Z1 : Iota), r Y X Z → r Z X Z1 → r Y (succ X) Z1) True % 3.68/3.85 Clause #2 (by assumption #[]): Eq (Not (Exists fun Z1 => Exists fun Z0 => And (r zero zero Z1) (r zero Z1 Z0))) True % 3.68/3.85 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r a zero (succ a)) True % 3.68/3.85 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 % 3.68/3.85 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 % 3.68/3.85 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 % 3.68/3.85 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 % 3.68/3.85 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) % 3.68/3.85 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)) % 3.68/3.85 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)) % 3.68/3.85 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) % 3.68/3.85 Clause #12 (by superposition #[11, 3]): ∀ (a : Iota), Or (Eq (r a (succ zero) (succ (succ a))) True) (Eq False True) % 3.68/3.85 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (r a (succ zero) (succ (succ a))) True % 3.68/3.85 Clause #15 (by clausification #[2]): Eq (Exists fun Z1 => Exists fun Z0 => And (r zero zero Z1) (r zero Z1 Z0)) False % 3.68/3.85 Clause #16 (by clausification #[15]): ∀ (a : Iota), Eq (Exists fun Z0 => And (r zero zero a) (r zero a Z0)) False % 3.68/3.85 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Eq (And (r zero zero a) (r zero a a_1)) False % 3.68/3.85 Clause #18 (by clausification #[17]): ∀ (a a_1 : Iota), Or (Eq (r zero zero a) False) (Eq (r zero a a_1) False) % 3.68/3.85 Clause #19 (by superposition #[18, 3]): ∀ (a : Iota), Or (Eq (r zero (succ zero) a) False) (Eq False True) % 3.68/3.85 Clause #22 (by clausification #[19]): ∀ (a : Iota), Eq (r zero (succ zero) a) False % 3.68/3.85 Clause #23 (by superposition #[22, 13]): Eq False True % 3.68/3.85 Clause #24 (by clausification #[23]): False % 3.68/3.85 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------