%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN055+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n026.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 08:07:04 PM UTC 2025 % Result : Theorem 3.45s 3.63s % Output : Proof 3.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN055+1 : TPTP v9.2.0. Released v2.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Oct 2 15:34:08 EDT 2025 % 0.13/0.35 % CPUTime : % 3.45/3.63 SZS status Theorem for theBenchmark.p % 3.45/3.63 SZS output start Proof for theBenchmark.p % 3.45/3.63 Clause #0 (by assumption #[]): Eq (Exists fun X => big_p X) True % 3.45/3.63 Clause #1 (by assumption #[]): Eq (∀ (X : Iota), big_f X → And (Not (big_g X)) (big_r X)) True % 3.45/3.63 Clause #2 (by assumption #[]): Eq (∀ (X : Iota), big_p X → And (big_g X) (big_f X)) True % 3.45/3.63 Clause #5 (by betaEtaReduce #[0]): Eq (Exists big_p) True % 3.45/3.63 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (big_p (skS.0 0 a)) True % 3.45/3.63 Clause #7 (by clausification #[2]): ∀ (a : Iota), Eq (big_p a → And (big_g a) (big_f a)) True % 3.45/3.63 Clause #8 (by clausification #[7]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (And (big_g a) (big_f a)) True) % 3.45/3.63 Clause #9 (by clausification #[8]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (big_f a) True) % 3.45/3.63 Clause #10 (by clausification #[8]): ∀ (a : Iota), Or (Eq (big_p a) False) (Eq (big_g a) True) % 3.45/3.63 Clause #11 (by superposition #[9, 6]): ∀ (a : Iota), Or (Eq (big_f (skS.0 0 a)) True) (Eq False True) % 3.45/3.63 Clause #12 (by superposition #[10, 6]): ∀ (a : Iota), Or (Eq (big_g (skS.0 0 a)) True) (Eq False True) % 3.45/3.63 Clause #13 (by clausification #[1]): ∀ (a : Iota), Eq (big_f a → And (Not (big_g a)) (big_r a)) True % 3.45/3.63 Clause #14 (by clausification #[13]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (And (Not (big_g a)) (big_r a)) True) % 3.45/3.63 Clause #16 (by clausification #[14]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (Not (big_g a)) True) % 3.45/3.63 Clause #17 (by clausification #[16]): ∀ (a : Iota), Or (Eq (big_f a) False) (Eq (big_g a) False) % 3.45/3.63 Clause #28 (by clausification #[11]): ∀ (a : Iota), Eq (big_f (skS.0 0 a)) True % 3.45/3.63 Clause #30 (by superposition #[28, 17]): ∀ (a : Iota), Or (Eq True False) (Eq (big_g (skS.0 0 a)) False) % 3.45/3.63 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (big_g (skS.0 0 a)) False % 3.45/3.63 Clause #33 (by clausification #[12]): ∀ (a : Iota), Eq (big_g (skS.0 0 a)) True % 3.45/3.63 Clause #34 (by superposition #[33, 31]): Eq True False % 3.45/3.63 Clause #36 (by clausification #[34]): False % 3.45/3.63 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------