%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO898_9 : TPTP v9.2.0. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 08:09:44 PM UTC 2025 % Result : Theorem 5.27s 5.51s % Output : Proof 5.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SYO898_9 : TPTP v9.2.0. Released v8.2.0. % 0.03/0.12 % Command : duper %s % 0.10/0.32 % Computer : n015.cluster.edu % 0.10/0.32 % Model : x86_64 x86_64 % 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.32 % Memory : 8042.1875MB % 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.32 % CPULimit : 300 % 0.10/0.32 % WCLimit : 300 % 0.10/0.32 % DateTime : Fri Oct 3 13:40:23 EDT 2025 % 0.10/0.33 % CPUTime : % 5.27/5.51 SZS status Theorem for theBenchmark.p % 5.27/5.51 SZS output start Proof for theBenchmark.p % 5.27/5.51 Clause #0 (by assumption #[]): Eq (∀ (W : «$ki_world»), Exists fun V => «$ki_accessible» W V) True % 5.27/5.51 Clause #1 (by assumption #[]): Eq % 5.27/5.51 (Not % 5.27/5.51 ((∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W) → % 5.27/5.51 Exists fun W => And («$ki_accessible» «$ki_local_world» W) (q W → p W))) % 5.27/5.51 True % 5.27/5.51 Clause #2 (by betaEtaReduce #[0]): Eq (∀ (W : «$ki_world»), Exists («$ki_accessible» W)) True % 5.27/5.51 Clause #3 (by clausification #[2]): ∀ (a : «$ki_world»), Eq (Exists («$ki_accessible» a)) True % 5.27/5.51 Clause #4 (by clausification #[3]): ∀ (a a_1 : «$ki_world»), Eq («$ki_accessible» a (skS.0 0 a a_1)) True % 5.27/5.51 Clause #5 (by clausification #[1]): Eq % 5.27/5.51 ((∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W) → % 5.27/5.51 Exists fun W => And («$ki_accessible» «$ki_local_world» W) (q W → p W)) % 5.27/5.51 False % 5.27/5.51 Clause #6 (by clausification #[5]): Eq (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W) True % 5.27/5.51 Clause #7 (by clausification #[5]): Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (q W → p W)) False % 5.27/5.51 Clause #8 (by clausification #[6]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» a → p a) True % 5.27/5.51 Clause #9 (by clausification #[8]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (p a) True) % 5.27/5.51 Clause #10 (by superposition #[9, 4]): ∀ (a : «$ki_world»), Or (Eq (p (skS.0 0 «$ki_local_world» a)) True) (Eq False True) % 5.27/5.51 Clause #11 (by clausification #[7]): ∀ (a : «$ki_world»), Eq (And («$ki_accessible» «$ki_local_world» a) (q a → p a)) False % 5.27/5.51 Clause #12 (by clausification #[11]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (q a → p a) False) % 5.27/5.51 Clause #14 (by clausification #[12]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (p a) False) % 5.27/5.51 Clause #16 (by superposition #[14, 4]): ∀ (a : «$ki_world»), Or (Eq (p (skS.0 0 «$ki_local_world» a)) False) (Eq False True) % 5.27/5.51 Clause #17 (by clausification #[16]): ∀ (a : «$ki_world»), Eq (p (skS.0 0 «$ki_local_world» a)) False % 5.27/5.51 Clause #18 (by clausification #[10]): ∀ (a : «$ki_world»), Eq (p (skS.0 0 «$ki_local_world» a)) True % 5.27/5.51 Clause #19 (by superposition #[18, 17]): Eq True False % 5.27/5.51 Clause #20 (by clausification #[19]): False % 5.27/5.51 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------