%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO887_22 : TPTP v9.2.0. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:09:42 PM UTC 2025 % Result : Theorem 3.62s 3.86s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SYO887_22 : TPTP v9.2.0. Released v8.2.0. % 0.07/0.12 % Command : duper %s % 0.12/0.34 % Computer : n008.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 13:17:08 EDT 2025 % 0.12/0.34 % CPUTime : % 3.62/3.86 SZS status Theorem for theBenchmark.p % 3.62/3.86 SZS output start Proof for theBenchmark.p % 3.62/3.86 Clause #0 (by assumption #[]): Eq (∀ (W : «$ki_world»), «$ki_accessible» W W) True % 3.62/3.86 Clause #4 (by assumption #[]): Eq % 3.62/3.86 (Not % 3.62/3.86 ((∀ (W : «$ki_world»), % 3.62/3.86 «$ki_accessible» «$ki_local_world» W → Exists fun X => And («$ki_exists_in_world_$i» W X) (f W X)) → % 3.62/3.86 Exists fun X => % 3.62/3.86 And («$ki_exists_in_world_$i» «$ki_local_world» X) % 3.62/3.86 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W X)))) % 3.62/3.86 True % 3.62/3.86 Clause #5 (by clausification #[0]): ∀ (a : «$ki_world»), Eq («$ki_accessible» a a) True % 3.62/3.86 Clause #22 (by clausification #[4]): Eq % 3.62/3.86 ((∀ (W : «$ki_world»), % 3.62/3.86 «$ki_accessible» «$ki_local_world» W → Exists fun X => And («$ki_exists_in_world_$i» W X) (f W X)) → % 3.62/3.86 Exists fun X => % 3.62/3.86 And («$ki_exists_in_world_$i» «$ki_local_world» X) % 3.62/3.86 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W X))) % 3.62/3.86 False % 3.62/3.86 Clause #23 (by clausification #[22]): Eq % 3.62/3.86 (∀ (W : «$ki_world»), % 3.62/3.86 «$ki_accessible» «$ki_local_world» W → Exists fun X => And («$ki_exists_in_world_$i» W X) (f W X)) % 3.62/3.86 True % 3.62/3.86 Clause #24 (by clausification #[22]): Eq % 3.62/3.86 (Exists fun X => % 3.62/3.86 And («$ki_exists_in_world_$i» «$ki_local_world» X) % 3.62/3.86 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W X))) % 3.62/3.86 False % 3.62/3.86 Clause #25 (by clausification #[23]): ∀ (a : «$ki_world»), % 3.62/3.86 Eq («$ki_accessible» «$ki_local_world» a → Exists fun X => And («$ki_exists_in_world_$i» a X) (f a X)) True % 3.62/3.86 Clause #26 (by clausification #[25]): ∀ (a : «$ki_world»), % 3.62/3.86 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.62/3.86 (Eq (Exists fun X => And («$ki_exists_in_world_$i» a X) (f a X)) True) % 3.62/3.86 Clause #27 (by clausification #[26]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.62/3.86 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.62/3.86 (Eq (And («$ki_exists_in_world_$i» a (skS.0 1 a a_1)) (f a (skS.0 1 a a_1))) True) % 3.62/3.86 Clause #28 (by clausification #[27]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (f a (skS.0 1 a a_1)) True) % 3.62/3.86 Clause #29 (by clausification #[27]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.62/3.86 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq («$ki_exists_in_world_$i» a (skS.0 1 a a_1)) True) % 3.62/3.86 Clause #30 (by superposition #[28, 5]): ∀ (a : Iota), Or (Eq (f «$ki_local_world» (skS.0 1 «$ki_local_world» a)) True) (Eq False True) % 3.62/3.86 Clause #31 (by clausification #[30]): ∀ (a : Iota), Eq (f «$ki_local_world» (skS.0 1 «$ki_local_world» a)) True % 3.62/3.86 Clause #32 (by superposition #[29, 5]): ∀ (a : Iota), Or (Eq («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 1 «$ki_local_world» a)) True) (Eq False True) % 3.62/3.86 Clause #33 (by clausification #[32]): ∀ (a : Iota), Eq («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 1 «$ki_local_world» a)) True % 3.62/3.86 Clause #37 (by clausification #[24]): ∀ (a : Iota), % 3.62/3.86 Eq % 3.62/3.86 (And («$ki_exists_in_world_$i» «$ki_local_world» a) % 3.62/3.86 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W a))) % 3.62/3.86 False % 3.62/3.86 Clause #38 (by clausification #[37]): ∀ (a : Iota), % 3.62/3.86 Or (Eq («$ki_exists_in_world_$i» «$ki_local_world» a) False) % 3.62/3.86 (Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (f W a)) False) % 3.62/3.86 Clause #39 (by clausification #[38]): ∀ (a : Iota) (a_1 : «$ki_world»), % 3.62/3.86 Or (Eq («$ki_exists_in_world_$i» «$ki_local_world» a) False) % 3.62/3.86 (Eq (And («$ki_accessible» «$ki_local_world» a_1) (f a_1 a)) False) % 3.62/3.86 Clause #40 (by clausification #[39]): ∀ (a : Iota) (a_1 : «$ki_world»), % 3.62/3.86 Or (Eq («$ki_exists_in_world_$i» «$ki_local_world» a) False) % 3.62/3.86 (Or (Eq («$ki_accessible» «$ki_local_world» a_1) False) (Eq (f a_1 a) False)) % 3.62/3.86 Clause #41 (by superposition #[40, 33]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.62/3.86 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.62/3.86 (Or (Eq (f a (skS.0 1 «$ki_local_world» a_1)) False) (Eq False True)) % 3.62/3.86 Clause #43 (by clausification #[41]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.62/3.86 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (f a (skS.0 1 «$ki_local_world» a_1)) False) % 3.62/3.87 Clause #44 (by superposition #[43, 5]): ∀ (a : Iota), Or (Eq (f «$ki_local_world» (skS.0 1 «$ki_local_world» a)) False) (Eq False True) % 3.62/3.87 Clause #45 (by clausification #[44]): ∀ (a : Iota), Eq (f «$ki_local_world» (skS.0 1 «$ki_local_world» a)) False % 3.62/3.87 Clause #46 (by superposition #[45, 31]): Eq False True % 3.62/3.87 Clause #47 (by clausification #[46]): False % 3.62/3.87 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------