%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO896_7 : TPTP v9.2.0. Released v8.2.0. % 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 08:09:44 PM UTC 2025 % Result : Theorem 4.03s 4.21s % Output : Proof 4.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SYO896_7 : TPTP v9.2.0. Released v8.2.0. % 0.08/0.14 % 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 : Fri Oct 3 12:56:38 EDT 2025 % 0.13/0.35 % CPUTime : % 4.03/4.21 SZS status Theorem for theBenchmark.p % 4.03/4.21 SZS output start Proof for theBenchmark.p % 4.03/4.21 Clause #0 (by assumption #[]): Eq % 4.03/4.21 (Not % 4.03/4.21 (And (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → q W) % 4.03/4.21 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → Not (q W)) → % 4.03/4.21 Not (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W)))) % 4.03/4.21 True % 4.03/4.21 Clause #1 (by clausification #[0]): Eq % 4.03/4.21 (And (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → q W) % 4.03/4.21 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → Not (q W)) → % 4.03/4.21 Not (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W))) % 4.03/4.21 False % 4.03/4.21 Clause #2 (by clausification #[1]): Eq % 4.03/4.21 (And (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → q W) % 4.03/4.21 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → Not (q W))) % 4.03/4.21 True % 4.03/4.21 Clause #3 (by clausification #[1]): Eq (Not (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W))) False % 4.03/4.21 Clause #4 (by clausification #[2]): Eq (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → Not (q W)) True % 4.03/4.21 Clause #5 (by clausification #[2]): Eq (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → p W → q W) True % 4.03/4.21 Clause #6 (by clausification #[4]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» a → p a → Not (q a)) True % 4.03/4.21 Clause #7 (by clausification #[6]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (p a → Not (q a)) True) % 4.03/4.21 Clause #8 (by clausification #[7]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Or (Eq (p a) False) (Eq (Not (q a)) True)) % 4.03/4.21 Clause #9 (by clausification #[8]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Or (Eq (p a) False) (Eq (q a) False)) % 4.03/4.21 Clause #10 (by clausification #[5]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» a → p a → q a) True % 4.03/4.21 Clause #11 (by clausification #[10]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (p a → q a) True) % 4.03/4.21 Clause #12 (by clausification #[11]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Or (Eq (p a) False) (Eq (q a) True)) % 4.03/4.21 Clause #13 (by clausification #[3]): Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W)) True % 4.03/4.21 Clause #14 (by clausification #[13]): ∀ (a : «$ki_world»), Eq (And («$ki_accessible» «$ki_local_world» (skS.0 0 a)) (p (skS.0 0 a))) True % 4.03/4.21 Clause #15 (by clausification #[14]): ∀ (a : «$ki_world»), Eq (p (skS.0 0 a)) True % 4.03/4.21 Clause #16 (by clausification #[14]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 0 a)) True % 4.03/4.21 Clause #17 (by superposition #[16, 9]): ∀ (a : «$ki_world»), Or (Eq True False) (Or (Eq (p (skS.0 0 a)) False) (Eq (q (skS.0 0 a)) False)) % 4.03/4.21 Clause #18 (by superposition #[16, 12]): ∀ (a : «$ki_world»), Or (Eq True False) (Or (Eq (p (skS.0 0 a)) False) (Eq (q (skS.0 0 a)) True)) % 4.03/4.21 Clause #19 (by clausification #[17]): ∀ (a : «$ki_world»), Or (Eq (p (skS.0 0 a)) False) (Eq (q (skS.0 0 a)) False) % 4.03/4.21 Clause #21 (by clausification #[18]): ∀ (a : «$ki_world»), Or (Eq (p (skS.0 0 a)) False) (Eq (q (skS.0 0 a)) True) % 4.03/4.21 Clause #22 (by superposition #[21, 15]): ∀ (a : «$ki_world»), Or (Eq (q (skS.0 0 a)) True) (Eq False True) % 4.03/4.21 Clause #23 (by clausification #[22]): ∀ (a : «$ki_world»), Eq (q (skS.0 0 a)) True % 4.03/4.21 Clause #24 (by backward demodulation #[23, 19]): ∀ (a : «$ki_world»), Or (Eq (p (skS.0 0 a)) False) (Eq True False) % 4.03/4.21 Clause #26 (by clausification #[24]): ∀ (a : «$ki_world»), Eq (p (skS.0 0 a)) False % 4.03/4.21 Clause #27 (by superposition #[26, 15]): Eq False True % 4.03/4.21 Clause #28 (by clausification #[27]): False % 4.03/4.21 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------