%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PLA053_2 : TPTP v9.2.0. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 07:58:04 PM UTC 2025 % Result : Theorem 3.66s 3.85s % Output : Proof 3.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.14 % Problem : PLA053_2 : TPTP v9.2.0. Released v8.2.0. % 0.03/0.15 % Command : duper %s % 0.15/0.37 % Computer : n019.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 300 % 0.15/0.37 % DateTime : Thu Oct 2 08:55:38 EDT 2025 % 0.15/0.38 % CPUTime : % 3.66/3.85 SZS status Theorem for theBenchmark.p % 3.66/3.85 SZS output start Proof for theBenchmark.p % 3.66/3.85 Clause #0 (by assumption #[]): Eq (∀ (W : «$ki_world»), «$ki_accessible» W W) True % 3.66/3.85 Clause #1 (by assumption #[]): Eq (∀ (W : «$ki_world») (X : Iota), «$ki_exists_in_world_$i» W X) True % 3.66/3.85 Clause #5 (by assumption #[]): Eq % 3.66/3.85 (∀ (W : «$ki_world»), % 3.66/3.85 «$ki_accessible» «$ki_local_world» W → % 3.66/3.85 ∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» W X → % 3.66/3.85 Exists fun D => % 3.66/3.85 And («$ki_exists_in_world_$i» W D) % 3.66/3.85 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 3.66/3.85 True % 3.66/3.85 Clause #6 (by assumption #[]): Eq % 3.66/3.85 (Not % 3.66/3.85 (∀ (W : «$ki_world»), % 3.66/3.85 «$ki_accessible» «$ki_local_world» W → % 3.66/3.85 ∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» W X → % 3.66/3.85 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X))) % 3.66/3.85 True % 3.66/3.85 Clause #7 (by clausification #[0]): ∀ (a : «$ki_world»), Eq («$ki_accessible» a a) True % 3.66/3.85 Clause #8 (by clausification #[1]): ∀ (a : «$ki_world»), Eq (∀ (X : Iota), «$ki_exists_in_world_$i» a X) True % 3.66/3.85 Clause #9 (by clausification #[8]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» a a_1) True % 3.66/3.85 Clause #34 (by clausification #[6]): Eq % 3.66/3.85 (∀ (W : «$ki_world»), % 3.66/3.85 «$ki_accessible» «$ki_local_world» W → % 3.66/3.85 ∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» W X → % 3.66/3.85 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X)) % 3.66/3.85 False % 3.66/3.85 Clause #35 (by clausification #[34]): ∀ (a : «$ki_world»), % 3.66/3.85 Eq % 3.66/3.85 (Not % 3.66/3.85 («$ki_accessible» «$ki_local_world» (skS.0 3 a) → % 3.66/3.85 ∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» (skS.0 3 a) X → % 3.66/3.85 Exists fun D => % 3.66/3.85 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 3.66/3.85 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X))) % 3.66/3.85 True % 3.66/3.85 Clause #36 (by clausification #[35]): ∀ (a : «$ki_world»), % 3.66/3.85 Eq % 3.66/3.85 («$ki_accessible» «$ki_local_world» (skS.0 3 a) → % 3.66/3.85 ∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» (skS.0 3 a) X → % 3.66/3.85 Exists fun D => % 3.66/3.85 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 3.66/3.85 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X)) % 3.66/3.85 False % 3.66/3.85 Clause #37 (by clausification #[36]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 3 a)) True % 3.66/3.85 Clause #38 (by clausification #[36]): ∀ (a : «$ki_world»), % 3.66/3.85 Eq % 3.66/3.85 (∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» (skS.0 3 a) X → % 3.66/3.85 Exists fun D => % 3.66/3.85 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 3.66/3.85 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X)) % 3.66/3.85 False % 3.66/3.85 Clause #41 (by clausification #[5]): ∀ (a : «$ki_world»), % 3.66/3.85 Eq % 3.66/3.85 («$ki_accessible» «$ki_local_world» a → % 3.66/3.85 ∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» a X → % 3.66/3.85 Exists fun D => % 3.66/3.85 And («$ki_exists_in_world_$i» a D) % 3.66/3.85 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 3.66/3.85 True % 3.66/3.85 Clause #42 (by clausification #[41]): ∀ (a : «$ki_world»), % 3.66/3.85 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.66/3.85 (Eq % 3.66/3.85 (∀ (X : Iota), % 3.66/3.85 «$ki_exists_in_world_$i» a X → % 3.66/3.85 Exists fun D => % 3.66/3.85 And («$ki_exists_in_world_$i» a D) % 3.66/3.85 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 3.66/3.85 True) % 3.66/3.85 Clause #43 (by clausification #[42]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.66/3.85 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.66/3.85 (Eq % 3.66/3.85 («$ki_exists_in_world_$i» a a_1 → % 3.66/3.85 Exists fun D => % 3.66/3.85 And («$ki_exists_in_world_$i» a D) % 3.66/3.85 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1)) % 3.66/3.85 True) % 3.66/3.85 Clause #44 (by clausification #[43]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.66/3.85 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.68/3.87 (Eq % 3.68/3.87 (Exists fun D => % 3.68/3.87 And («$ki_exists_in_world_$i» a D) % 3.68/3.87 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1)) % 3.68/3.87 True)) % 3.68/3.87 Clause #45 (by clausification #[44]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.68/3.87 (Eq % 3.68/3.87 (And («$ki_exists_in_world_$i» a (skS.0 4 a a_1 a_2)) % 3.68/3.87 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 (skS.0 4 a a_1 a_2)) → defused W0 a_1)) % 3.68/3.87 True)) % 3.68/3.87 Clause #46 (by clausification #[45]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.68/3.87 (Eq (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 (skS.0 4 a a_1 a_2)) → defused W0 a_1) % 3.68/3.87 True)) % 3.68/3.87 Clause #48 (by clausification #[46]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.68/3.87 (Eq («$ki_accessible» a a_2 → And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True)) % 3.68/3.87 Clause #49 (by clausification #[48]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.68/3.87 (Or (Eq («$ki_accessible» a a_2) False) % 3.68/3.87 (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True))) % 3.68/3.87 Clause #50 (by clausification #[49]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.68/3.87 (Or (Eq («$ki_accessible» a a_2) False) % 3.68/3.87 (Or (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3))) False) (Eq (defused a_2 a_1) True)))) % 3.68/3.87 Clause #51 (by clausification #[50]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.68/3.87 (Or (Eq («$ki_accessible» a a_2) False) % 3.68/3.87 (Or (Eq (defused a_2 a_1) True) (Or (Eq (bomb a_2 a_1) False) (Eq (h a_2 (skS.0 4 a a_1 a_3)) False))))) % 3.68/3.87 Clause #52 (by forward demodulation #[51, 9]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq True False) % 3.68/3.87 (Or (Eq («$ki_accessible» a a_1) False) % 3.68/3.87 (Or (Eq (defused a_1 a_2) True) (Or (Eq (bomb a_1 a_2) False) (Eq (h a_1 (skS.0 4 a a_2 a_3)) False))))) % 3.68/3.87 Clause #53 (by clausification #[52]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq («$ki_accessible» a a_1) False) % 3.68/3.87 (Or (Eq (defused a_1 a_2) True) (Or (Eq (bomb a_1 a_2) False) (Eq (h a_1 (skS.0 4 a a_2 a_3)) False)))) % 3.68/3.87 Clause #55 (by superposition #[53, 7]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.87 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.87 (Or (Eq (defused a a_1) True) % 3.68/3.87 (Or (Eq (bomb a a_1) False) (Or (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True)))) % 3.68/3.87 Clause #61 (by clausification #[38]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.68/3.87 Eq % 3.68/3.87 (Not % 3.68/3.87 («$ki_exists_in_world_$i» (skS.0 3 a) (skS.0 5 a a_1) → % 3.68/3.87 Exists fun D => % 3.68/3.87 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 3.68/3.87 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1)))) % 3.68/3.87 True % 3.68/3.87 Clause #62 (by clausification #[61]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.68/3.87 Eq % 3.68/3.87 («$ki_exists_in_world_$i» (skS.0 3 a) (skS.0 5 a a_1) → % 3.68/3.87 Exists fun D => % 3.68/3.87 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 3.68/3.87 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1))) % 3.68/3.89 False % 3.68/3.89 Clause #64 (by clausification #[62]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.68/3.89 Eq % 3.68/3.89 (Exists fun D => % 3.68/3.89 And («$ki_exists_in_world_$i» (skS.0 3 a) D) % 3.68/3.89 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1))) % 3.68/3.89 False % 3.68/3.89 Clause #66 (by clausification #[55]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.68/3.89 (Or (Eq (defused a a_1) True) (Or (Eq (bomb a a_1) False) (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False))) % 3.68/3.89 Clause #67 (by superposition #[66, 37]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq (defused (skS.0 3 a) a_1) True) % 3.68/3.89 (Or (Eq (bomb (skS.0 3 a) a_1) False) % 3.68/3.89 (Or (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True))) % 3.68/3.89 Clause #73 (by clausification #[64]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Eq % 3.68/3.89 (And («$ki_exists_in_world_$i» (skS.0 3 a) a_1) % 3.68/3.89 (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1) → defused (skS.0 3 a) (skS.0 5 a a_2))) % 3.68/3.89 False % 3.68/3.89 Clause #74 (by clausification #[73]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) % 3.68/3.89 (Eq (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1) → defused (skS.0 3 a) (skS.0 5 a a_2)) False) % 3.68/3.89 Clause #75 (by clausification #[74]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) % 3.68/3.89 (Eq (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1)) True) % 3.68/3.89 Clause #76 (by clausification #[74]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (defused (skS.0 3 a) (skS.0 5 a a_2)) False) % 3.68/3.89 Clause #77 (by clausification #[75]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (h (skS.0 3 a) a_1) True) % 3.68/3.89 Clause #78 (by clausification #[75]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (bomb (skS.0 3 a) (skS.0 5 a a_2)) True) % 3.68/3.89 Clause #79 (by forward demodulation #[77, 9]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (h (skS.0 3 a) a_1) True) % 3.68/3.89 Clause #80 (by clausification #[79]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (h (skS.0 3 a) a_1) True % 3.68/3.89 Clause #81 (by superposition #[78, 9]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (bomb (skS.0 3 a) (skS.0 5 a a_1)) True) (Eq False True) % 3.68/3.89 Clause #82 (by clausification #[81]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (bomb (skS.0 3 a) (skS.0 5 a a_1)) True % 3.68/3.89 Clause #84 (by superposition #[76, 9]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) False) (Eq False True) % 3.68/3.89 Clause #85 (by clausification #[84]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) False % 3.68/3.89 Clause #92 (by clausification #[67]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq (defused (skS.0 3 a) a_1) True) % 3.68/3.89 (Or (Eq (bomb (skS.0 3 a) a_1) False) (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False)) % 3.68/3.89 Clause #94 (by superposition #[92, 82]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) True) % 3.68/3.89 (Or (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) (Eq False True)) % 3.68/3.89 Clause #102 (by clausification #[94]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) True) % 3.68/3.89 (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) % 3.68/3.89 Clause #103 (by forward demodulation #[102, 85]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.68/3.89 Or (Eq False True) (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) % 3.68/3.89 Clause #104 (by clausification #[103]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False % 3.68/3.89 Clause #105 (by superposition #[104, 80]): Eq False True % 3.68/3.89 Clause #106 (by clausification #[105]): False % 3.68/3.89 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------