%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO018^1 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:08:25 PM UTC 2025 % Result : Theorem 3.56s 3.72s % Output : Proof 3.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO018^1 : TPTP v9.2.0. Released v3.7.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n008.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 14:21:38 EDT 2025 % 0.13/0.34 % CPUTime : % 3.56/3.72 SZS status Theorem for theBenchmark.p % 3.56/3.72 SZS output start Proof for theBenchmark.p % 3.56/3.72 Clause #0 (by assumption #[]): Eq (Not ((p fun X => f (And (a fun X => f b X) b) X) → p (f (And b (a (f b)))))) True % 3.56/3.72 Clause #1 (by betaEtaReduce #[0]): Eq (Not (p (f (And (a (f b)) b)) → p (f (And b (a (f b)))))) True % 3.56/3.72 Clause #2 (by clausification #[1]): Eq (p (f (And (a (f b)) b)) → p (f (And b (a (f b))))) False % 3.56/3.72 Clause #3 (by clausification #[2]): Eq (p (f (And (a (f b)) b))) True % 3.56/3.72 Clause #4 (by clausification #[2]): Eq (p (f (And b (a (f b))))) False % 3.56/3.72 Clause #5 (by identity loobHoist #[3]): Or (Eq (p (f True)) True) (Eq (And (a (f b)) b) False) % 3.56/3.72 Clause #6 (by identity boolHoist #[3]): Or (Eq (p (f False)) True) (Eq (And (a (f b)) b) True) % 3.56/3.72 Clause #7 (by clausification #[5]): Or (Eq (p (f True)) True) (Or (Eq (a (f b)) False) (Eq b False)) % 3.56/3.72 Clause #8 (by identity loobHoist #[7]): Or (Eq (p (f True)) True) (Or (Eq b False) (Or (Eq (a (f True)) False) (Eq b False))) % 3.56/3.72 Clause #10 (by eliminate duplicate literals #[8]): Or (Eq (p (f True)) True) (Or (Eq b False) (Eq (a (f True)) False)) % 3.56/3.72 Clause #11 (by identity loobHoist #[4]): Or (Eq (p (f True)) False) (Eq (And b (a (f b))) False) % 3.56/3.72 Clause #12 (by identity boolHoist #[4]): Or (Eq (p (f False)) False) (Eq (And b (a (f b))) True) % 3.56/3.72 Clause #13 (by clausification #[11]): Or (Eq (p (f True)) False) (Or (Eq b False) (Eq (a (f b)) False)) % 3.56/3.72 Clause #14 (by identity loobHoist #[13]): Or (Eq (p (f True)) False) (Or (Eq b False) (Or (Eq (a (f True)) False) (Eq b False))) % 3.56/3.72 Clause #16 (by eliminate duplicate literals #[14]): Or (Eq (p (f True)) False) (Or (Eq b False) (Eq (a (f True)) False)) % 3.56/3.72 Clause #17 (by clausification #[6]): Or (Eq (p (f False)) True) (Eq b True) % 3.56/3.72 Clause #18 (by clausification #[6]): Or (Eq (p (f False)) True) (Eq (a (f b)) True) % 3.56/3.72 Clause #19 (by identity loobHoist #[18]): Or (Eq (p (f False)) True) (Or (Eq (a (f True)) True) (Eq b False)) % 3.56/3.72 Clause #21 (by clausification #[12]): Or (Eq (p (f False)) False) (Eq (a (f b)) True) % 3.56/3.72 Clause #22 (by clausification #[12]): Or (Eq (p (f False)) False) (Eq b True) % 3.56/3.72 Clause #23 (by identity loobHoist #[21]): Or (Eq (p (f False)) False) (Or (Eq (a (f True)) True) (Eq b False)) % 3.56/3.72 Clause #26 (by superposition #[22, 17]): Or (Eq b True) (Or (Eq False True) (Eq b True)) % 3.56/3.72 Clause #27 (by clausification #[26]): Or (Eq b True) (Eq b True) % 3.56/3.72 Clause #28 (by eliminate duplicate literals #[27]): Eq b True % 3.56/3.72 Clause #29 (by backward demodulation #[28, 10]): Or (Eq (p (f True)) True) (Or (Eq True False) (Eq (a (f True)) False)) % 3.56/3.72 Clause #30 (by backward demodulation #[28, 16]): Or (Eq (p (f True)) False) (Or (Eq True False) (Eq (a (f True)) False)) % 3.56/3.72 Clause #32 (by backward demodulation #[28, 19]): Or (Eq (p (f False)) True) (Or (Eq (a (f True)) True) (Eq True False)) % 3.56/3.72 Clause #33 (by backward demodulation #[28, 23]): Or (Eq (p (f False)) False) (Or (Eq (a (f True)) True) (Eq True False)) % 3.56/3.72 Clause #36 (by clausification #[29]): Or (Eq (p (f True)) True) (Eq (a (f True)) False) % 3.56/3.72 Clause #37 (by clausification #[30]): Or (Eq (p (f True)) False) (Eq (a (f True)) False) % 3.56/3.72 Clause #38 (by clausification #[33]): Or (Eq (p (f False)) False) (Eq (a (f True)) True) % 3.56/3.72 Clause #40 (by clausification #[32]): Or (Eq (p (f False)) True) (Eq (a (f True)) True) % 3.56/3.72 Clause #41 (by superposition #[40, 38]): Or (Eq (a (f True)) True) (Or (Eq True False) (Eq (a (f True)) True)) % 3.56/3.72 Clause #42 (by clausification #[41]): Or (Eq (a (f True)) True) (Eq (a (f True)) True) % 3.56/3.72 Clause #43 (by eliminate duplicate literals #[42]): Eq (a (f True)) True % 3.56/3.72 Clause #44 (by backward demodulation #[43, 36]): Or (Eq (p (f True)) True) (Eq True False) % 3.56/3.72 Clause #45 (by backward demodulation #[43, 37]): Or (Eq (p (f True)) False) (Eq True False) % 3.56/3.72 Clause #46 (by clausification #[45]): Eq (p (f True)) False % 3.56/3.72 Clause #47 (by clausification #[44]): Eq (p (f True)) True % 3.56/3.72 Clause #48 (by superposition #[47, 46]): Eq True False % 3.56/3.72 Clause #49 (by clausification #[48]): False % 3.56/3.72 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------