%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO500^1 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 08:09:12 PM UTC 2025 % Result : Theorem 3.47s 3.67s % Output : Proof 3.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SYO500^1 : TPTP v9.2.0. Released v4.0.0. % 0.03/0.13 % Command : duper %s % 0.13/0.34 % Computer : n031.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 : Fri Oct 3 14:31:08 EDT 2025 % 0.13/0.34 % CPUTime : % 3.47/3.67 SZS status Theorem for theBenchmark.p % 3.47/3.67 SZS output start Proof for theBenchmark.p % 3.47/3.67 Clause #0 (by assumption #[]): Eq (Not (Eq (f (f (f x))) (f x))) True % 3.47/3.67 Clause #1 (by clausification #[0]): Eq (Eq (f (f (f x))) (f x)) False % 3.47/3.67 Clause #2 (by clausification #[1]): Ne (f (f (f x))) (f x) % 3.47/3.67 Clause #3 (by clausification #[2]): Or (Eq (f (f (f x))) False) (Eq (f x) False) % 3.47/3.67 Clause #4 (by clausification #[2]): Or (Eq (f (f (f x))) True) (Eq (f x) True) % 3.47/3.67 Clause #5 (by identity loobHoist #[3]): Or (Eq (f x) False) (Or (Eq (f True) False) (Eq (f (f x)) False)) % 3.47/3.67 Clause #6 (by identity boolHoist #[3]): Or (Eq (f x) False) (Or (Eq (f False) False) (Eq (f (f x)) True)) % 3.47/3.67 Clause #7 (by identity loobHoist #[5]): Or (Eq (f True) False) (Or (Eq (f (f x)) False) (Or (Eq (f True) False) (Eq x False))) % 3.47/3.67 Clause #8 (by identity boolHoist #[5]): Or (Eq (f True) False) (Or (Eq (f (f x)) False) (Or (Eq (f False) False) (Eq x True))) % 3.47/3.67 Clause #9 (by eliminate duplicate literals #[7]): Or (Eq (f True) False) (Or (Eq (f (f x)) False) (Eq x False)) % 3.47/3.67 Clause #10 (by identity loobHoist #[9]): Or (Eq (f True) False) (Or (Eq x False) (Or (Eq (f True) False) (Eq (f x) False))) % 3.47/3.67 Clause #12 (by eliminate duplicate literals #[10]): Or (Eq (f True) False) (Or (Eq x False) (Eq (f x) False)) % 3.47/3.67 Clause #13 (by identity loobHoist #[12]): Or (Eq (f True) False) (Or (Eq x False) (Or (Eq (f True) False) (Eq x False))) % 3.47/3.67 Clause #15 (by eliminate duplicate literals #[13]): Or (Eq (f True) False) (Eq x False) % 3.47/3.67 Clause #16 (by identity loobHoist #[4]): Or (Eq (f x) True) (Or (Eq (f True) True) (Eq (f (f x)) False)) % 3.47/3.67 Clause #17 (by identity boolHoist #[4]): Or (Eq (f x) True) (Or (Eq (f False) True) (Eq (f (f x)) True)) % 3.47/3.67 Clause #18 (by identity loobHoist #[16]): Or (Eq (f True) True) (Or (Eq (f (f x)) False) (Or (Eq (f True) True) (Eq x False))) % 3.47/3.67 Clause #20 (by eliminate duplicate literals #[18]): Or (Eq (f True) True) (Or (Eq (f (f x)) False) (Eq x False)) % 3.47/3.67 Clause #22 (by identity boolHoist #[20]): Or (Eq (f True) True) (Or (Eq x False) (Or (Eq (f False) False) (Eq (f x) True))) % 3.47/3.67 Clause #23 (by identity loobHoist #[17]): Or (Eq (f False) True) (Or (Eq (f (f x)) True) (Or (Eq (f True) True) (Eq x False))) % 3.47/3.67 Clause #24 (by identity boolHoist #[17]): Or (Eq (f False) True) (Or (Eq (f (f x)) True) (Or (Eq (f False) True) (Eq x True))) % 3.47/3.67 Clause #26 (by identity boolHoist #[23]): Or (Eq (f False) True) (Or (Eq (f True) True) (Or (Eq x False) (Or (Eq (f False) True) (Eq (f x) True)))) % 3.47/3.67 Clause #31 (by identity boolHoist #[6]): Or (Eq (f False) False) (Or (Eq (f (f x)) True) (Or (Eq (f False) False) (Eq x True))) % 3.47/3.67 Clause #32 (by identity loobHoist #[8]): Or (Eq (f True) False) (Or (Eq (f False) False) (Or (Eq x True) (Or (Eq (f True) False) (Eq (f x) False)))) % 3.47/3.67 Clause #34 (by eliminate duplicate literals #[32]): Or (Eq (f True) False) (Or (Eq (f False) False) (Or (Eq x True) (Eq (f x) False))) % 3.47/3.67 Clause #36 (by identity boolHoist #[34]): Or (Eq (f True) False) (Or (Eq (f False) False) (Or (Eq x True) (Or (Eq (f False) False) (Eq x True)))) % 3.47/3.67 Clause #37 (by identity loobHoist #[22]): Or (Eq (f True) True) (Or (Eq x False) (Or (Eq (f False) False) (Or (Eq (f True) True) (Eq x False)))) % 3.47/3.67 Clause #39 (by eliminate duplicate literals #[37]): Or (Eq (f True) True) (Or (Eq x False) (Eq (f False) False)) % 3.47/3.67 Clause #42 (by eliminate duplicate literals #[31]): Or (Eq (f False) False) (Or (Eq (f (f x)) True) (Eq x True)) % 3.47/3.67 Clause #43 (by identity loobHoist #[42]): Or (Eq (f False) False) (Or (Eq x True) (Or (Eq (f True) True) (Eq (f x) False))) % 3.47/3.67 Clause #46 (by identity boolHoist #[43]): Or (Eq (f False) False) (Or (Eq x True) (Or (Eq (f True) True) (Or (Eq (f False) False) (Eq x True)))) % 3.47/3.67 Clause #47 (by eliminate duplicate literals #[24]): Or (Eq (f False) True) (Or (Eq (f (f x)) True) (Eq x True)) % 3.47/3.67 Clause #49 (by identity boolHoist #[47]): Or (Eq (f False) True) (Or (Eq x True) (Or (Eq (f False) True) (Eq (f x) True))) % 3.47/3.67 Clause #52 (by eliminate duplicate literals #[49]): Or (Eq (f False) True) (Or (Eq x True) (Eq (f x) True)) % 3.47/3.67 Clause #54 (by identity boolHoist #[52]): Or (Eq (f False) True) (Or (Eq x True) (Or (Eq (f False) True) (Eq x True))) % 3.51/3.68 Clause #55 (by eliminate duplicate literals #[54]): Or (Eq (f False) True) (Eq x True) % 3.51/3.68 Clause #56 (by eliminate duplicate literals #[36]): Or (Eq (f True) False) (Or (Eq (f False) False) (Eq x True)) % 3.51/3.68 Clause #57 (by eliminate duplicate literals #[46]): Or (Eq (f False) False) (Or (Eq x True) (Eq (f True) True)) % 3.51/3.68 Clause #58 (by superposition #[57, 55]): Or (Eq x True) (Or (Eq (f True) True) (Or (Eq False True) (Eq x True))) % 3.51/3.68 Clause #59 (by clausification #[58]): Or (Eq x True) (Or (Eq (f True) True) (Eq x True)) % 3.51/3.68 Clause #60 (by eliminate duplicate literals #[59]): Or (Eq x True) (Eq (f True) True) % 3.51/3.68 Clause #62 (by superposition #[60, 56]): Or (Eq x True) (Or (Eq True False) (Or (Eq (f False) False) (Eq x True))) % 3.51/3.68 Clause #63 (by eliminate duplicate literals #[26]): Or (Eq (f False) True) (Or (Eq (f True) True) (Or (Eq x False) (Eq (f x) True))) % 3.51/3.68 Clause #64 (by identity loobHoist #[63]): Or (Eq (f False) True) (Or (Eq (f True) True) (Or (Eq x False) (Or (Eq (f True) True) (Eq x False)))) % 3.51/3.68 Clause #66 (by eliminate duplicate literals #[64]): Or (Eq (f False) True) (Or (Eq (f True) True) (Eq x False)) % 3.51/3.68 Clause #68 (by clausification #[62]): Or (Eq x True) (Or (Eq (f False) False) (Eq x True)) % 3.51/3.68 Clause #69 (by eliminate duplicate literals #[68]): Or (Eq x True) (Eq (f False) False) % 3.51/3.68 Clause #70 (by superposition #[69, 55]): Or (Eq x True) (Or (Eq False True) (Eq x True)) % 3.51/3.68 Clause #71 (by clausification #[70]): Or (Eq x True) (Eq x True) % 3.51/3.68 Clause #72 (by eliminate duplicate literals #[71]): Eq x True % 3.51/3.68 Clause #73 (by backward demodulation #[72, 15]): Or (Eq (f True) False) (Eq True False) % 3.51/3.68 Clause #74 (by backward demodulation #[72, 39]): Or (Eq (f True) True) (Or (Eq True False) (Eq (f False) False)) % 3.51/3.68 Clause #77 (by backward demodulation #[72, 66]): Or (Eq (f False) True) (Or (Eq (f True) True) (Eq True False)) % 3.51/3.68 Clause #79 (by clausification #[73]): Eq (f True) False % 3.51/3.68 Clause #80 (by clausification #[74]): Or (Eq (f True) True) (Eq (f False) False) % 3.51/3.68 Clause #81 (by forward demodulation #[80, 79]): Or (Eq False True) (Eq (f False) False) % 3.51/3.68 Clause #82 (by clausification #[81]): Eq (f False) False % 3.51/3.68 Clause #83 (by clausification #[77]): Or (Eq (f False) True) (Eq (f True) True) % 3.51/3.68 Clause #84 (by forward demodulation #[83, 79]): Or (Eq (f False) True) (Eq False True) % 3.51/3.68 Clause #85 (by clausification #[84]): Eq (f False) True % 3.51/3.68 Clause #86 (by superposition #[85, 82]): Eq True False % 3.51/3.68 Clause #87 (by clausification #[86]): False % 3.51/3.68 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------