%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO902_8 : 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 3.43s 3.67s % Output : Proof 3.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SYO902_8 : TPTP v9.2.0. Released v8.2.0. % 0.10/0.13 % Command : duper %s % 0.13/0.34 % Computer : n026.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 12:50:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.43/3.67 SZS status Theorem for theBenchmark.p % 3.43/3.67 SZS output start Proof for theBenchmark.p % 3.43/3.67 Clause #0 (by assumption #[]): Eq (∀ (W : «$ki_world»), «$ki_accessible» W W) True % 3.43/3.67 Clause #1 (by assumption #[]): Eq % 3.43/3.67 (Not % 3.43/3.67 ((Exists fun W => % 3.43/3.67 And («$ki_accessible» «$ki_local_world» W) % 3.43/3.67 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → Exists fun W1 => And («$ki_accessible» W0 W1) (p W1))) → % 3.43/3.67 Exists fun W => And («$ki_accessible» «$ki_local_world» W) (Exists fun W0 => And («$ki_accessible» W W0) (p W0)))) % 3.43/3.67 True % 3.43/3.67 Clause #2 (by clausification #[0]): ∀ (a : «$ki_world»), Eq («$ki_accessible» a a) True % 3.43/3.67 Clause #3 (by clausification #[1]): Eq % 3.43/3.67 ((Exists fun W => % 3.43/3.67 And («$ki_accessible» «$ki_local_world» W) % 3.43/3.67 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → Exists fun W1 => And («$ki_accessible» W0 W1) (p W1))) → % 3.43/3.67 Exists fun W => And («$ki_accessible» «$ki_local_world» W) (Exists fun W0 => And («$ki_accessible» W W0) (p W0))) % 3.43/3.67 False % 3.43/3.67 Clause #4 (by clausification #[3]): Eq % 3.43/3.67 (Exists fun W => % 3.43/3.67 And («$ki_accessible» «$ki_local_world» W) % 3.43/3.67 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → Exists fun W1 => And («$ki_accessible» W0 W1) (p W1))) % 3.43/3.67 True % 3.43/3.67 Clause #5 (by clausification #[3]): Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (Exists fun W0 => And («$ki_accessible» W W0) (p W0))) % 3.43/3.67 False % 3.43/3.67 Clause #6 (by clausification #[4]): ∀ (a : «$ki_world»), % 3.43/3.67 Eq % 3.43/3.67 (And («$ki_accessible» «$ki_local_world» (skS.0 0 a)) % 3.43/3.67 (∀ (W0 : «$ki_world»), «$ki_accessible» (skS.0 0 a) W0 → Exists fun W1 => And («$ki_accessible» W0 W1) (p W1))) % 3.43/3.67 True % 3.43/3.67 Clause #7 (by clausification #[6]): ∀ (a : «$ki_world»), % 3.43/3.67 Eq (∀ (W0 : «$ki_world»), «$ki_accessible» (skS.0 0 a) W0 → Exists fun W1 => And («$ki_accessible» W0 W1) (p W1)) True % 3.43/3.67 Clause #8 (by clausification #[6]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 0 a)) True % 3.43/3.67 Clause #9 (by clausification #[7]): ∀ (a a_1 : «$ki_world»), % 3.43/3.67 Eq («$ki_accessible» (skS.0 0 a) a_1 → Exists fun W1 => And («$ki_accessible» a_1 W1) (p W1)) True % 3.43/3.67 Clause #10 (by clausification #[9]): ∀ (a a_1 : «$ki_world»), % 3.43/3.67 Or (Eq («$ki_accessible» (skS.0 0 a) a_1) False) (Eq (Exists fun W1 => And («$ki_accessible» a_1 W1) (p W1)) True) % 3.43/3.67 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : «$ki_world»), % 3.43/3.67 Or (Eq («$ki_accessible» (skS.0 0 a) a_1) False) % 3.43/3.67 (Eq (And («$ki_accessible» a_1 (skS.0 1 a_1 a_2)) (p (skS.0 1 a_1 a_2))) True) % 3.43/3.67 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : «$ki_world»), Or (Eq («$ki_accessible» (skS.0 0 a) a_1) False) (Eq (p (skS.0 1 a_1 a_2)) True) % 3.43/3.67 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : «$ki_world»), % 3.43/3.67 Or (Eq («$ki_accessible» (skS.0 0 a) a_1) False) (Eq («$ki_accessible» a_1 (skS.0 1 a_1 a_2)) True) % 3.43/3.67 Clause #14 (by superposition #[12, 2]): ∀ (a a_1 : «$ki_world»), Or (Eq (p (skS.0 1 (skS.0 0 a) a_1)) True) (Eq False True) % 3.43/3.67 Clause #15 (by clausification #[5]): ∀ (a : «$ki_world»), % 3.43/3.67 Eq (And («$ki_accessible» «$ki_local_world» a) (Exists fun W0 => And («$ki_accessible» a W0) (p W0))) False % 3.43/3.67 Clause #16 (by clausification #[15]): ∀ (a : «$ki_world»), % 3.43/3.67 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (Exists fun W0 => And («$ki_accessible» a W0) (p W0)) False) % 3.43/3.67 Clause #17 (by clausification #[16]): ∀ (a a_1 : «$ki_world»), % 3.43/3.67 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (And («$ki_accessible» a a_1) (p a_1)) False) % 3.43/3.67 Clause #18 (by clausification #[17]): ∀ (a a_1 : «$ki_world»), % 3.43/3.67 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Or (Eq («$ki_accessible» a a_1) False) (Eq (p a_1) False)) % 3.43/3.67 Clause #19 (by superposition #[18, 8]): ∀ (a a_1 : «$ki_world»), Or (Eq («$ki_accessible» (skS.0 0 a) a_1) False) (Or (Eq (p a_1) False) (Eq False True)) % 3.43/3.67 Clause #24 (by superposition #[13, 2]): ∀ (a a_1 : «$ki_world»), Or (Eq («$ki_accessible» (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) True) (Eq False True) % 3.43/3.67 Clause #27 (by clausification #[19]): ∀ (a a_1 : «$ki_world»), Or (Eq («$ki_accessible» (skS.0 0 a) a_1) False) (Eq (p a_1) False) % 3.43/3.67 Clause #28 (by clausification #[14]): ∀ (a a_1 : «$ki_world»), Eq (p (skS.0 1 (skS.0 0 a) a_1)) True % 3.43/3.67 Clause #29 (by clausification #[24]): ∀ (a a_1 : «$ki_world»), Eq («$ki_accessible» (skS.0 0 a) (skS.0 1 (skS.0 0 a) a_1)) True % 3.43/3.67 Clause #32 (by superposition #[29, 27]): ∀ (a a_1 : «$ki_world»), Or (Eq True False) (Eq (p (skS.0 1 (skS.0 0 a) a_1)) False) % 3.43/3.67 Clause #34 (by clausification #[32]): ∀ (a a_1 : «$ki_world»), Eq (p (skS.0 1 (skS.0 0 a) a_1)) False % 3.43/3.67 Clause #35 (by superposition #[34, 28]): Eq False True % 3.43/3.67 Clause #36 (by clausification #[35]): False % 3.43/3.67 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------