%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN986+1.003 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n023.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 3.69s 3.88s % Output : Proof 3.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN986+1.003 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n023.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 15:10:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.69/3.88 SZS status Theorem for theBenchmark.p % 3.69/3.88 SZS output start Proof for theBenchmark.p % 3.69/3.88 Clause #0 (by assumption #[]): Eq (∀ (Y : Iota), r Y zero (succ Y)) True % 3.69/3.88 Clause #1 (by assumption #[]): Eq (∀ (Y X Z Z1 : Iota), r Y X Z → r Z X Z1 → r Y (succ X) Z1) True % 3.69/3.88 Clause #2 (by assumption #[]): Eq % 3.69/3.88 (Not % 3.69/3.88 (Exists fun Z3 => % 3.69/3.88 Exists fun Z2 => % 3.69/3.88 Exists fun Z1 => % 3.69/3.88 Exists fun Z0 => And (And (And (r zero zero Z3) (r zero Z3 Z2)) (r zero Z2 Z1)) (r zero Z1 Z0))) % 3.69/3.88 True % 3.69/3.88 Clause #3 (by clausification #[0]): ∀ (a : Iota), Eq (r a zero (succ a)) True % 3.69/3.88 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 % 3.69/3.88 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 % 3.69/3.88 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 % 3.69/3.88 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 % 3.69/3.88 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) % 3.69/3.88 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)) % 3.69/3.88 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)) % 3.69/3.88 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) % 3.69/3.88 Clause #12 (by superposition #[11, 3]): ∀ (a : Iota), Or (Eq (r a (succ zero) (succ (succ a))) True) (Eq False True) % 3.69/3.88 Clause #13 (by clausification #[12]): ∀ (a : Iota), Eq (r a (succ zero) (succ (succ a))) True % 3.69/3.88 Clause #14 (by superposition #[13, 9]): ∀ (a a_1 : Iota), % 3.69/3.88 Or (Eq True False) (Or (Eq (r (succ (succ a)) (succ zero) a_1) False) (Eq (r a (succ (succ zero)) a_1) True)) % 3.69/3.88 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) % 3.69/3.88 Clause #16 (by superposition #[15, 13]): ∀ (a : Iota), Or (Eq (r a (succ (succ zero)) (succ (succ (succ (succ a))))) True) (Eq False True) % 3.69/3.88 Clause #17 (by clausification #[2]): Eq % 3.69/3.88 (Exists fun Z3 => % 3.69/3.88 Exists fun Z2 => % 3.69/3.88 Exists fun Z1 => Exists fun Z0 => And (And (And (r zero zero Z3) (r zero Z3 Z2)) (r zero Z2 Z1)) (r zero Z1 Z0)) % 3.69/3.88 False % 3.69/3.88 Clause #18 (by clausification #[17]): ∀ (a : Iota), % 3.69/3.88 Eq % 3.69/3.88 (Exists fun Z2 => % 3.69/3.88 Exists fun Z1 => Exists fun Z0 => And (And (And (r zero zero a) (r zero a Z2)) (r zero Z2 Z1)) (r zero Z1 Z0)) % 3.69/3.88 False % 3.69/3.88 Clause #19 (by clausification #[18]): ∀ (a a_1 : Iota), % 3.69/3.88 Eq (Exists fun Z1 => Exists fun Z0 => And (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 Z1)) (r zero Z1 Z0)) % 3.69/3.88 False % 3.69/3.88 Clause #20 (by clausification #[19]): ∀ (a a_1 a_2 : Iota), % 3.69/3.88 Eq (Exists fun Z0 => And (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 a_2)) (r zero a_2 Z0)) False % 3.69/3.88 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 a_3 : Iota), Eq (And (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 a_2)) (r zero a_2 a_3)) False % 3.69/3.88 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.88 Or (Eq (And (And (r zero zero a) (r zero a a_1)) (r zero a_1 a_2)) False) (Eq (r zero a_2 a_3) False) % 3.69/3.88 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.88 Or (Eq (r zero a a_1) False) (Or (Eq (And (r zero zero a_2) (r zero a_2 a_3)) False) (Eq (r zero a_3 a) False)) % 3.69/3.88 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 a_3 : Iota), % 3.69/3.88 Or (Eq (r zero a a_1) False) % 3.69/3.88 (Or (Eq (r zero a_2 a) False) (Or (Eq (r zero zero a_3) False) (Eq (r zero a_3 a_2) False))) % 3.69/3.88 Clause #27 (by clausification #[16]): ∀ (a : Iota), Eq (r a (succ (succ zero)) (succ (succ (succ (succ a))))) True % 3.69/3.88 Clause #28 (by superposition #[27, 9]): ∀ (a a_1 : Iota), % 3.69/3.88 Or (Eq True False) % 3.69/3.88 (Or (Eq (r (succ (succ (succ (succ a)))) (succ (succ zero)) a_1) False) % 3.69/3.88 (Eq (r a (succ (succ (succ zero))) a_1) True)) % 3.69/3.89 Clause #36 (by clausification #[28]): ∀ (a a_1 : Iota), % 3.69/3.89 Or (Eq (r (succ (succ (succ (succ a)))) (succ (succ zero)) a_1) False) (Eq (r a (succ (succ (succ zero))) a_1) True) % 3.69/3.89 Clause #37 (by superposition #[36, 27]): ∀ (a : Iota), % 3.69/3.89 Or (Eq (r a (succ (succ (succ zero))) (succ (succ (succ (succ (succ (succ (succ (succ a))))))))) True) (Eq False True) % 3.69/3.89 Clause #38 (by clausification #[37]): ∀ (a : Iota), Eq (r a (succ (succ (succ zero))) (succ (succ (succ (succ (succ (succ (succ (succ a))))))))) True % 3.69/3.89 Clause #39 (by superposition #[38, 9]): ∀ (a a_1 : Iota), % 3.69/3.89 Or (Eq True False) % 3.69/3.89 (Or (Eq (r (succ (succ (succ (succ (succ (succ (succ (succ a)))))))) (succ (succ (succ zero))) a_1) False) % 3.69/3.89 (Eq (r a (succ (succ (succ (succ zero)))) a_1) True)) % 3.69/3.89 Clause #47 (by clausification #[39]): ∀ (a a_1 : Iota), % 3.69/3.89 Or (Eq (r (succ (succ (succ (succ (succ (succ (succ (succ a)))))))) (succ (succ (succ zero))) a_1) False) % 3.69/3.89 (Eq (r a (succ (succ (succ (succ zero)))) a_1) True) % 3.69/3.89 Clause #48 (by superposition #[47, 38]): ∀ (a : Iota), % 3.69/3.89 Or % 3.69/3.89 (Eq % 3.69/3.89 (r a (succ (succ (succ (succ zero)))) % 3.69/3.89 (succ % 3.69/3.89 (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ a))))))))))))))))) % 3.69/3.89 True) % 3.69/3.89 (Eq False True) % 3.69/3.89 Clause #49 (by clausification #[48]): ∀ (a : Iota), % 3.69/3.89 Eq % 3.69/3.89 (r a (succ (succ (succ (succ zero)))) % 3.69/3.89 (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ (succ a))))))))))))))))) % 3.69/3.89 True % 3.69/3.89 Clause #51 (by superposition #[49, 24]): ∀ (a a_1 : Iota), % 3.69/3.89 Or (Eq True False) % 3.69/3.89 (Or (Eq (r zero a (succ (succ (succ (succ zero))))) False) % 3.69/3.89 (Or (Eq (r zero zero a_1) False) (Eq (r zero a_1 a) False))) % 3.69/3.89 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), % 3.69/3.89 Or (Eq (r zero a (succ (succ (succ (succ zero))))) False) (Or (Eq (r zero zero a_1) False) (Eq (r zero a_1 a) False)) % 3.69/3.89 Clause #53 (by superposition #[52, 27]): ∀ (a : Iota), Or (Eq (r zero zero a) False) (Or (Eq (r zero a (succ (succ zero))) False) (Eq False True)) % 3.69/3.89 Clause #54 (by clausification #[53]): ∀ (a : Iota), Or (Eq (r zero zero a) False) (Eq (r zero a (succ (succ zero))) False) % 3.69/3.89 Clause #55 (by superposition #[54, 3]): Or (Eq (r zero (succ zero) (succ (succ zero))) False) (Eq False True) % 3.69/3.89 Clause #56 (by clausification #[55]): Eq (r zero (succ zero) (succ (succ zero))) False % 3.69/3.89 Clause #57 (by superposition #[56, 13]): Eq False True % 3.69/3.89 Clause #58 (by clausification #[57]): False % 3.69/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------