%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYN397+1 : TPTP v9.2.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 08:07:35 PM UTC 2025 % Result : Theorem 3.86s 4.03s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SYN397+1 : TPTP v9.2.0. Released v2.0.0. % 0.08/0.14 % Command : duper %s % 0.15/0.36 % Computer : n013.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Thu Oct 2 15:11:08 EDT 2025 % 0.15/0.36 % CPUTime : % 3.86/4.03 SZS status Theorem for theBenchmark.p % 3.86/4.03 SZS output start Proof for theBenchmark.p % 3.86/4.03 Clause #0 (by assumption #[]): Eq (Not (Iff (Not (Exists fun X => f X)) (∀ (Y : Iota), Not (f Y)))) True % 3.86/4.03 Clause #1 (by betaEtaReduce #[0]): Eq (Not (Iff (Not (Exists f)) (∀ (Y : Iota), Not (f Y)))) True % 3.86/4.03 Clause #2 (by clausification #[1]): Eq (Iff (Not (Exists f)) (∀ (Y : Iota), Not (f Y))) False % 3.86/4.03 Clause #3 (by clausification #[2]): Or (Eq (Not (Exists f)) False) (Eq (∀ (Y : Iota), Not (f Y)) False) % 3.86/4.03 Clause #4 (by clausification #[2]): Or (Eq (Not (Exists f)) True) (Eq (∀ (Y : Iota), Not (f Y)) True) % 3.86/4.03 Clause #5 (by clausification #[3]): Or (Eq (∀ (Y : Iota), Not (f Y)) False) (Eq (Exists f) True) % 3.86/4.03 Clause #6 (by clausification #[5]): ∀ (a : Iota), Or (Eq (Exists f) True) (Eq (Not (Not (f (skS.0 0 a)))) True) % 3.86/4.03 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Or (Eq (Not (Not (f (skS.0 0 a)))) True) (Eq (f (skS.0 1 a_1)) True) % 3.86/4.03 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (Not (f (skS.0 0 a_1))) False) % 3.86/4.03 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (f (skS.0 0 a_1)) True) % 3.86/4.03 Clause #10 (by clausification #[4]): Or (Eq (∀ (Y : Iota), Not (f Y)) True) (Eq (Exists f) False) % 3.86/4.03 Clause #11 (by clausification #[10]): ∀ (a : Iota), Or (Eq (Exists f) False) (Eq (Not (f a)) True) % 3.86/4.03 Clause #12 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (Not (f a)) True) (Eq (f a_1) False) % 3.86/4.03 Clause #13 (by clausification #[12]): ∀ (a a_1 : Iota), Or (Eq (f a) False) (Eq (f a_1) False) % 3.86/4.03 Clause #15 (by superposition #[13, 9]): ∀ (a a_1 : Iota), Or (Eq (f a) False) (Or (Eq (f (skS.0 1 a_1)) True) (Eq False True)) % 3.86/4.03 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (f a) False) (Eq (f (skS.0 1 a_1)) True) % 3.86/4.03 Clause #18 (by superposition #[16, 9]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq (f (skS.0 1 a_1)) True) (Eq False True)) % 3.86/4.03 Clause #22 (by clausification #[18]): ∀ (a a_1 : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq (f (skS.0 1 a_1)) True) % 3.86/4.03 Clause #26 (by equality factoring #[22]): ∀ (a : Iota), Or (Ne True True) (Eq (f (skS.0 1 a)) True) % 3.86/4.03 Clause #27 (by clausification #[26]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) True) (Or (Eq True False) (Eq True False)) % 3.86/4.03 Clause #29 (by clausification #[27]): ∀ (a : Iota), Or (Eq (f (skS.0 1 a)) True) (Eq True False) % 3.86/4.03 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (f (skS.0 1 a)) True % 3.86/4.03 Clause #31 (by superposition #[30, 13]): ∀ (a : Iota), Or (Eq True False) (Eq (f a) False) % 3.86/4.03 Clause #33 (by clausification #[31]): ∀ (a : Iota), Eq (f a) False % 3.86/4.03 Clause #34 (by superposition #[33, 30]): Eq False True % 3.86/4.03 Clause #35 (by clausification #[34]): False % 3.86/4.03 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------