%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SYO891_16 : TPTP v9.2.0. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:09:43 PM UTC 2025 % Result : Theorem 3.71s 3.97s % Output : Proof 3.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SYO891_16 : TPTP v9.2.0. Released v8.2.0. % 0.11/0.13 % Command : duper %s % 0.13/0.34 % Computer : n027.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 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 14:32:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.71/3.97 SZS status Theorem for theBenchmark.p % 3.71/3.97 SZS output start Proof for theBenchmark.p % 3.71/3.97 Clause #2 (by assumption #[]): Eq % 3.71/3.97 (∀ (W V : «$ki_world») (X : Iota), % 3.71/3.97 And («$ki_exists_in_world_$i» W X) («$ki_accessible» W V) → «$ki_exists_in_world_$i» V X) % 3.71/3.97 True % 3.71/3.97 Clause #8 (by assumption #[]): Eq % 3.71/3.97 (Not % 3.71/3.97 ((∀ (X : Iota), % 3.71/3.97 «$ki_exists_in_world_$i» «$ki_local_world» X → % 3.71/3.97 ∀ (W : «$ki_world»), % 3.71/3.97 «$ki_accessible» «$ki_local_world» W → Exists fun Y => And («$ki_exists_in_world_$i» W Y) (qmltpeq W X Y)) → % 3.71/3.97 (Exists fun X => % 3.71/3.97 And («$ki_exists_in_world_$i» «$ki_local_world» X) % 3.71/3.97 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X))) → % 3.71/3.97 Exists fun W => % 3.71/3.97 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X)))) % 3.71/3.97 True % 3.71/3.97 Clause #16 (by clausification #[2]): ∀ (a : «$ki_world»), % 3.71/3.97 Eq % 3.71/3.97 (∀ (V : «$ki_world») (X : Iota), % 3.71/3.97 And («$ki_exists_in_world_$i» a X) («$ki_accessible» a V) → «$ki_exists_in_world_$i» V X) % 3.71/3.97 True % 3.71/3.97 Clause #17 (by clausification #[16]): ∀ (a a_1 : «$ki_world»), % 3.71/3.97 Eq (∀ (X : Iota), And («$ki_exists_in_world_$i» a X) («$ki_accessible» a a_1) → «$ki_exists_in_world_$i» a_1 X) True % 3.71/3.97 Clause #18 (by clausification #[17]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»), % 3.71/3.97 Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2) → «$ki_exists_in_world_$i» a_2 a_1) True % 3.71/3.97 Clause #19 (by clausification #[18]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»), % 3.71/3.97 Or (Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2)) False) % 3.71/3.97 (Eq («$ki_exists_in_world_$i» a_2 a_1) True) % 3.71/3.97 Clause #20 (by clausification #[19]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»), % 3.71/3.97 Or (Eq («$ki_exists_in_world_$i» a a_1) True) % 3.71/3.97 (Or (Eq («$ki_exists_in_world_$i» a_2 a_1) False) (Eq («$ki_accessible» a_2 a) False)) % 3.71/3.97 Clause #53 (by clausification #[8]): Eq % 3.71/3.97 ((∀ (X : Iota), % 3.71/3.97 «$ki_exists_in_world_$i» «$ki_local_world» X → % 3.71/3.97 ∀ (W : «$ki_world»), % 3.71/3.97 «$ki_accessible» «$ki_local_world» W → Exists fun Y => And («$ki_exists_in_world_$i» W Y) (qmltpeq W X Y)) → % 3.71/3.97 (Exists fun X => % 3.71/3.97 And («$ki_exists_in_world_$i» «$ki_local_world» X) % 3.71/3.97 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X))) → % 3.71/3.97 Exists fun W => % 3.71/3.97 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X))) % 3.71/3.97 False % 3.71/3.97 Clause #55 (by clausification #[53]): Eq % 3.71/3.97 ((Exists fun X => % 3.71/3.97 And («$ki_exists_in_world_$i» «$ki_local_world» X) % 3.71/3.97 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X))) → % 3.71/3.97 Exists fun W => % 3.71/3.97 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X))) % 3.71/3.97 False % 3.71/3.97 Clause #64 (by clausification #[55]): Eq % 3.71/3.97 (Exists fun X => % 3.71/3.97 And («$ki_exists_in_world_$i» «$ki_local_world» X) % 3.71/3.97 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X))) % 3.71/3.97 True % 3.71/3.97 Clause #65 (by clausification #[55]): Eq % 3.71/3.97 (Exists fun W => % 3.71/3.97 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X))) % 3.71/3.97 False % 3.71/3.97 Clause #66 (by clausification #[64]): ∀ (a : Iota), % 3.71/3.97 Eq % 3.71/3.97 (And («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 2 a)) % 3.71/3.97 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W (skS.0 2 a)))) % 3.71/3.97 True % 3.71/3.97 Clause #67 (by clausification #[66]): ∀ (a : Iota), Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W (skS.0 2 a))) True % 3.71/3.97 Clause #68 (by clausification #[66]): ∀ (a : Iota), Eq («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 2 a)) True % 3.71/3.97 Clause #69 (by clausification #[67]): ∀ (a : Iota) (a_1 : «$ki_world»), % 3.71/3.97 Eq (And («$ki_accessible» «$ki_local_world» (skS.0 3 a a_1)) (p (skS.0 3 a a_1) (skS.0 2 a))) True % 3.71/3.97 Clause #70 (by clausification #[69]): ∀ (a : Iota) (a_1 : «$ki_world»), Eq (p (skS.0 3 a a_1) (skS.0 2 a)) True % 3.80/3.98 Clause #71 (by clausification #[69]): ∀ (a : Iota) (a_1 : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 3 a a_1)) True % 3.80/3.98 Clause #77 (by superposition #[68, 20]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.80/3.98 Or (Eq («$ki_exists_in_world_$i» a (skS.0 2 a_1)) True) % 3.80/3.98 (Or (Eq True False) (Eq («$ki_accessible» «$ki_local_world» a) False)) % 3.80/3.98 Clause #80 (by clausification #[77]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.80/3.98 Or (Eq («$ki_exists_in_world_$i» a (skS.0 2 a_1)) True) (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.80/3.98 Clause #81 (by superposition #[80, 71]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), % 3.80/3.98 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a a_1) (skS.0 2 a_2)) True) (Eq False True) % 3.80/3.98 Clause #87 (by clausification #[81]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), Eq («$ki_exists_in_world_$i» (skS.0 3 a a_1) (skS.0 2 a_2)) True % 3.80/3.98 Clause #89 (by clausification #[65]): ∀ (a : «$ki_world»), % 3.80/3.98 Eq (And («$ki_accessible» «$ki_local_world» a) (Exists fun X => And («$ki_exists_in_world_$i» a X) (p a X))) False % 3.80/3.98 Clause #90 (by clausification #[89]): ∀ (a : «$ki_world»), % 3.80/3.98 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.80/3.98 (Eq (Exists fun X => And («$ki_exists_in_world_$i» a X) (p a X)) False) % 3.80/3.98 Clause #91 (by clausification #[90]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.80/3.98 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (And («$ki_exists_in_world_$i» a a_1) (p a a_1)) False) % 3.80/3.98 Clause #92 (by clausification #[91]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.80/3.98 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.80/3.98 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) (Eq (p a a_1) False)) % 3.80/3.98 Clause #93 (by superposition #[92, 71]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), % 3.80/3.98 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a a_1) a_2) False) (Or (Eq (p (skS.0 3 a a_1) a_2) False) (Eq False True)) % 3.80/3.98 Clause #110 (by clausification #[93]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), % 3.80/3.98 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a a_1) a_2) False) (Eq (p (skS.0 3 a a_1) a_2) False) % 3.80/3.98 Clause #111 (by superposition #[110, 87]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), Or (Eq (p (skS.0 3 a a_1) (skS.0 2 a_2)) False) (Eq False True) % 3.80/3.98 Clause #114 (by clausification #[111]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), Eq (p (skS.0 3 a a_1) (skS.0 2 a_2)) False % 3.80/3.98 Clause #115 (by superposition #[114, 70]): Eq False True % 3.80/3.98 Clause #116 (by clausification #[115]): False % 3.80/3.98 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------