%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : PLA053_4 : TPTP v9.2.0. Released v8.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n007.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 3.61s 3.77s % Output : Proof 3.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : PLA053_4 : TPTP v9.2.0. Released v8.2.0. % 0.03/0.13 % Command : duper %s % 0.14/0.34 % Computer : n007.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Oct 2 08:57:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.61/3.77 SZS status Theorem for theBenchmark.p % 3.61/3.77 SZS output start Proof for theBenchmark.p % 3.61/3.77 Clause #0 (by assumption #[]): Eq (∀ (W : «$ki_world»), «$ki_accessible» W W) True % 3.61/3.77 Clause #2 (by assumption #[]): Eq (∀ (W : «$ki_world») (X : Iota), «$ki_exists_in_world_$i» W X) True % 3.61/3.77 Clause #6 (by assumption #[]): Eq % 3.61/3.77 (∀ (W : «$ki_world»), % 3.61/3.77 «$ki_accessible» «$ki_local_world» W → % 3.61/3.77 ∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» W X → % 3.61/3.77 Exists fun D => % 3.61/3.77 And («$ki_exists_in_world_$i» W D) % 3.61/3.77 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 3.61/3.77 True % 3.61/3.77 Clause #7 (by assumption #[]): Eq % 3.61/3.77 (Not % 3.61/3.77 (∀ (W : «$ki_world»), % 3.61/3.77 «$ki_accessible» «$ki_local_world» W → % 3.61/3.77 ∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» W X → % 3.61/3.77 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X))) % 3.61/3.77 True % 3.61/3.77 Clause #8 (by clausification #[0]): ∀ (a : «$ki_world»), Eq («$ki_accessible» a a) True % 3.61/3.77 Clause #9 (by clausification #[2]): ∀ (a : «$ki_world»), Eq (∀ (X : Iota), «$ki_exists_in_world_$i» a X) True % 3.61/3.77 Clause #10 (by clausification #[9]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» a a_1) True % 3.61/3.77 Clause #28 (by clausification #[7]): Eq % 3.61/3.77 (∀ (W : «$ki_world»), % 3.61/3.77 «$ki_accessible» «$ki_local_world» W → % 3.61/3.77 ∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» W X → % 3.61/3.77 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X)) % 3.61/3.77 False % 3.61/3.77 Clause #29 (by clausification #[28]): ∀ (a : «$ki_world»), % 3.61/3.77 Eq % 3.61/3.77 (Not % 3.61/3.77 («$ki_accessible» «$ki_local_world» (skS.0 2 a) → % 3.61/3.77 ∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» (skS.0 2 a) X → % 3.61/3.77 Exists fun D => % 3.61/3.77 And («$ki_exists_in_world_$i» (skS.0 2 a) D) % 3.61/3.77 (And (bomb (skS.0 2 a) X) (h (skS.0 2 a) D) → defused (skS.0 2 a) X))) % 3.61/3.77 True % 3.61/3.77 Clause #30 (by clausification #[29]): ∀ (a : «$ki_world»), % 3.61/3.77 Eq % 3.61/3.77 («$ki_accessible» «$ki_local_world» (skS.0 2 a) → % 3.61/3.77 ∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» (skS.0 2 a) X → % 3.61/3.77 Exists fun D => % 3.61/3.77 And («$ki_exists_in_world_$i» (skS.0 2 a) D) % 3.61/3.77 (And (bomb (skS.0 2 a) X) (h (skS.0 2 a) D) → defused (skS.0 2 a) X)) % 3.61/3.77 False % 3.61/3.77 Clause #31 (by clausification #[30]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 2 a)) True % 3.61/3.77 Clause #32 (by clausification #[30]): ∀ (a : «$ki_world»), % 3.61/3.77 Eq % 3.61/3.77 (∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» (skS.0 2 a) X → % 3.61/3.77 Exists fun D => % 3.61/3.77 And («$ki_exists_in_world_$i» (skS.0 2 a) D) % 3.61/3.77 (And (bomb (skS.0 2 a) X) (h (skS.0 2 a) D) → defused (skS.0 2 a) X)) % 3.61/3.77 False % 3.61/3.77 Clause #52 (by clausification #[6]): ∀ (a : «$ki_world»), % 3.61/3.77 Eq % 3.61/3.77 («$ki_accessible» «$ki_local_world» a → % 3.61/3.77 ∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» a X → % 3.61/3.77 Exists fun D => % 3.61/3.77 And («$ki_exists_in_world_$i» a D) % 3.61/3.77 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 3.61/3.77 True % 3.61/3.77 Clause #53 (by clausification #[52]): ∀ (a : «$ki_world»), % 3.61/3.77 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.61/3.77 (Eq % 3.61/3.77 (∀ (X : Iota), % 3.61/3.77 «$ki_exists_in_world_$i» a X → % 3.61/3.77 Exists fun D => % 3.61/3.77 And («$ki_exists_in_world_$i» a D) % 3.61/3.77 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X)) % 3.61/3.77 True) % 3.61/3.77 Clause #54 (by clausification #[53]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.61/3.77 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.61/3.77 (Eq % 3.61/3.77 («$ki_exists_in_world_$i» a a_1 → % 3.61/3.77 Exists fun D => % 3.61/3.77 And («$ki_exists_in_world_$i» a D) % 3.61/3.77 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1)) % 3.61/3.77 True) % 3.61/3.77 Clause #55 (by clausification #[54]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.61/3.77 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.63/3.79 (Eq % 3.63/3.79 (Exists fun D => % 3.63/3.79 And («$ki_exists_in_world_$i» a D) % 3.63/3.79 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1)) % 3.63/3.79 True)) % 3.63/3.79 Clause #56 (by clausification #[55]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.63/3.79 (Eq % 3.63/3.79 (And («$ki_exists_in_world_$i» a (skS.0 4 a a_1 a_2)) % 3.63/3.79 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 (skS.0 4 a a_1 a_2)) → defused W0 a_1)) % 3.63/3.79 True)) % 3.63/3.79 Clause #57 (by clausification #[56]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.63/3.79 (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) % 3.63/3.79 True)) % 3.63/3.79 Clause #59 (by clausification #[57]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.63/3.79 (Eq («$ki_accessible» a a_2 → And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True)) % 3.63/3.79 Clause #60 (by clausification #[59]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.63/3.79 (Or (Eq («$ki_accessible» a a_2) False) % 3.63/3.79 (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True))) % 3.63/3.79 Clause #61 (by clausification #[60]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.63/3.79 (Or (Eq («$ki_accessible» a a_2) False) % 3.63/3.79 (Or (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3))) False) (Eq (defused a_2 a_1) True)))) % 3.63/3.79 Clause #62 (by clausification #[61]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) % 3.63/3.79 (Or (Eq («$ki_accessible» a a_2) False) % 3.63/3.79 (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))))) % 3.63/3.79 Clause #63 (by forward demodulation #[62, 10]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq True False) % 3.63/3.79 (Or (Eq («$ki_accessible» a a_1) False) % 3.63/3.79 (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))))) % 3.63/3.79 Clause #64 (by clausification #[63]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq («$ki_accessible» a a_1) False) % 3.63/3.79 (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)))) % 3.63/3.79 Clause #66 (by superposition #[64, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.79 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.79 (Or (Eq (defused a a_1) True) % 3.63/3.79 (Or (Eq (bomb a a_1) False) (Or (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True)))) % 3.63/3.79 Clause #72 (by clausification #[32]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.63/3.79 Eq % 3.63/3.79 (Not % 3.63/3.79 («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 5 a a_1) → % 3.63/3.79 Exists fun D => % 3.63/3.79 And («$ki_exists_in_world_$i» (skS.0 2 a) D) % 3.63/3.79 (And (bomb (skS.0 2 a) (skS.0 5 a a_1)) (h (skS.0 2 a) D) → defused (skS.0 2 a) (skS.0 5 a a_1)))) % 3.63/3.79 True % 3.63/3.79 Clause #73 (by clausification #[72]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.63/3.79 Eq % 3.63/3.79 («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 5 a a_1) → % 3.63/3.79 Exists fun D => % 3.63/3.79 And («$ki_exists_in_world_$i» (skS.0 2 a) D) % 3.63/3.79 (And (bomb (skS.0 2 a) (skS.0 5 a a_1)) (h (skS.0 2 a) D) → defused (skS.0 2 a) (skS.0 5 a a_1))) % 3.63/3.81 False % 3.63/3.81 Clause #75 (by clausification #[73]): ∀ (a : «$ki_world») (a_1 : Iota), % 3.63/3.81 Eq % 3.63/3.81 (Exists fun D => % 3.63/3.81 And («$ki_exists_in_world_$i» (skS.0 2 a) D) % 3.63/3.81 (And (bomb (skS.0 2 a) (skS.0 5 a a_1)) (h (skS.0 2 a) D) → defused (skS.0 2 a) (skS.0 5 a a_1))) % 3.63/3.81 False % 3.63/3.81 Clause #77 (by clausification #[66]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq («$ki_accessible» «$ki_local_world» a) False) % 3.63/3.81 (Or (Eq (defused a a_1) True) (Or (Eq (bomb a a_1) False) (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False))) % 3.63/3.81 Clause #78 (by superposition #[77, 31]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq (defused (skS.0 2 a) a_1) True) % 3.63/3.81 (Or (Eq (bomb (skS.0 2 a) a_1) False) % 3.63/3.81 (Or (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True))) % 3.63/3.81 Clause #82 (by clausification #[75]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Eq % 3.63/3.81 (And («$ki_exists_in_world_$i» (skS.0 2 a) a_1) % 3.63/3.81 (And (bomb (skS.0 2 a) (skS.0 5 a a_2)) (h (skS.0 2 a) a_1) → defused (skS.0 2 a) (skS.0 5 a a_2))) % 3.63/3.81 False % 3.63/3.81 Clause #83 (by clausification #[82]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) % 3.63/3.81 (Eq (And (bomb (skS.0 2 a) (skS.0 5 a a_2)) (h (skS.0 2 a) a_1) → defused (skS.0 2 a) (skS.0 5 a a_2)) False) % 3.63/3.81 Clause #84 (by clausification #[83]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) % 3.63/3.81 (Eq (And (bomb (skS.0 2 a) (skS.0 5 a a_2)) (h (skS.0 2 a) a_1)) True) % 3.63/3.81 Clause #85 (by clausification #[83]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) (Eq (defused (skS.0 2 a) (skS.0 5 a a_2)) False) % 3.63/3.81 Clause #86 (by clausification #[84]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) (Eq (h (skS.0 2 a) a_1) True) % 3.63/3.81 Clause #87 (by clausification #[84]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) (Eq (bomb (skS.0 2 a) (skS.0 5 a a_2)) True) % 3.63/3.81 Clause #88 (by forward demodulation #[86, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (h (skS.0 2 a) a_1) True) % 3.63/3.81 Clause #89 (by clausification #[88]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (h (skS.0 2 a) a_1) True % 3.63/3.81 Clause #90 (by superposition #[87, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (bomb (skS.0 2 a) (skS.0 5 a a_1)) True) (Eq False True) % 3.63/3.81 Clause #93 (by clausification #[90]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (bomb (skS.0 2 a) (skS.0 5 a a_1)) True % 3.63/3.81 Clause #95 (by superposition #[85, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) False) (Eq False True) % 3.63/3.81 Clause #96 (by clausification #[95]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) False % 3.63/3.81 Clause #103 (by clausification #[78]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq (defused (skS.0 2 a) a_1) True) % 3.63/3.81 (Or (Eq (bomb (skS.0 2 a) a_1) False) (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False)) % 3.63/3.81 Clause #105 (by superposition #[103, 93]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) True) % 3.63/3.81 (Or (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) (Eq False True)) % 3.63/3.81 Clause #113 (by clausification #[105]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) True) % 3.63/3.81 (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) % 3.63/3.81 Clause #114 (by forward demodulation #[113, 96]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), % 3.63/3.81 Or (Eq False True) (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) % 3.63/3.81 Clause #115 (by clausification #[114]): ∀ (a : «$ki_world») (a_1 a_2 : Iota), Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False % 3.63/3.81 Clause #116 (by superposition #[115, 89]): Eq False True % 3.63/3.81 Clause #117 (by clausification #[116]): False % 3.63/3.81 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------