TSTP Solution File: PLA053_2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n024.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 : Thu Aug 31 13:00:19 EDT 2023
% Result : Theorem 4.01s 4.20s
% Output : Proof 4.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 06:09:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.01/4.20 SZS status Theorem for theBenchmark.p
% 4.01/4.20 SZS output start Proof for theBenchmark.p
% 4.01/4.20 Clause #0 (by assumption #[]): Eq (∀ (W : «$ki_world»), «$ki_accessible» W W) True
% 4.01/4.20 Clause #1 (by assumption #[]): Eq (∀ (W : «$ki_world») (X : Iota), «$ki_exists_in_world_$i» W X) True
% 4.01/4.20 Clause #5 (by assumption #[]): Eq
% 4.01/4.20 (∀ (W : «$ki_world»),
% 4.01/4.20 «$ki_accessible» «$ki_local_world» W →
% 4.01/4.20 ∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» W X →
% 4.01/4.20 Exists fun D =>
% 4.01/4.20 And («$ki_exists_in_world_$i» W D)
% 4.01/4.20 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → And (bomb W0 X) (h W0 D) → defused W0 X))
% 4.01/4.20 True
% 4.01/4.20 Clause #6 (by assumption #[]): Eq
% 4.01/4.20 (Not
% 4.01/4.20 (∀ (W : «$ki_world»),
% 4.01/4.20 «$ki_accessible» «$ki_local_world» W →
% 4.01/4.20 ∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» W X →
% 4.01/4.20 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X)))
% 4.01/4.20 True
% 4.01/4.20 Clause #7 (by clausification #[0]): ∀ (a : «$ki_world»), Eq («$ki_accessible» a a) True
% 4.01/4.20 Clause #8 (by clausification #[1]): ∀ (a : «$ki_world»), Eq (∀ (X : Iota), «$ki_exists_in_world_$i» a X) True
% 4.01/4.20 Clause #9 (by clausification #[8]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» a a_1) True
% 4.01/4.20 Clause #34 (by clausification #[6]): Eq
% 4.01/4.20 (∀ (W : «$ki_world»),
% 4.01/4.20 «$ki_accessible» «$ki_local_world» W →
% 4.01/4.20 ∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» W X →
% 4.01/4.20 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X))
% 4.01/4.20 False
% 4.01/4.20 Clause #35 (by clausification #[34]): ∀ (a : «$ki_world»),
% 4.01/4.20 Eq
% 4.01/4.20 (Not
% 4.01/4.20 («$ki_accessible» «$ki_local_world» (skS.0 3 a) →
% 4.01/4.20 ∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» (skS.0 3 a) X →
% 4.01/4.20 Exists fun D =>
% 4.01/4.20 And («$ki_exists_in_world_$i» (skS.0 3 a) D)
% 4.01/4.20 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X)))
% 4.01/4.20 True
% 4.01/4.20 Clause #36 (by clausification #[35]): ∀ (a : «$ki_world»),
% 4.01/4.20 Eq
% 4.01/4.20 («$ki_accessible» «$ki_local_world» (skS.0 3 a) →
% 4.01/4.20 ∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» (skS.0 3 a) X →
% 4.01/4.20 Exists fun D =>
% 4.01/4.20 And («$ki_exists_in_world_$i» (skS.0 3 a) D)
% 4.01/4.20 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X))
% 4.01/4.20 False
% 4.01/4.20 Clause #37 (by clausification #[36]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 3 a)) True
% 4.01/4.20 Clause #38 (by clausification #[36]): ∀ (a : «$ki_world»),
% 4.01/4.20 Eq
% 4.01/4.20 (∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» (skS.0 3 a) X →
% 4.01/4.20 Exists fun D =>
% 4.01/4.20 And («$ki_exists_in_world_$i» (skS.0 3 a) D)
% 4.01/4.20 (And (bomb (skS.0 3 a) X) (h (skS.0 3 a) D) → defused (skS.0 3 a) X))
% 4.01/4.20 False
% 4.01/4.20 Clause #41 (by clausification #[5]): ∀ (a : «$ki_world»),
% 4.01/4.20 Eq
% 4.01/4.20 («$ki_accessible» «$ki_local_world» a →
% 4.01/4.20 ∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» a X →
% 4.01/4.20 Exists fun D =>
% 4.01/4.20 And («$ki_exists_in_world_$i» a D)
% 4.01/4.20 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X))
% 4.01/4.20 True
% 4.01/4.20 Clause #42 (by clausification #[41]): ∀ (a : «$ki_world»),
% 4.01/4.20 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.01/4.20 (Eq
% 4.01/4.20 (∀ (X : Iota),
% 4.01/4.20 «$ki_exists_in_world_$i» a X →
% 4.01/4.20 Exists fun D =>
% 4.01/4.20 And («$ki_exists_in_world_$i» a D)
% 4.01/4.20 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X))
% 4.01/4.20 True)
% 4.01/4.20 Clause #43 (by clausification #[42]): ∀ (a : «$ki_world») (a_1 : Iota),
% 4.01/4.20 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.01/4.20 (Eq
% 4.01/4.20 («$ki_exists_in_world_$i» a a_1 →
% 4.01/4.20 Exists fun D =>
% 4.01/4.20 And («$ki_exists_in_world_$i» a D)
% 4.01/4.20 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1))
% 4.01/4.20 True)
% 4.01/4.20 Clause #44 (by clausification #[43]): ∀ (a : «$ki_world») (a_1 : Iota),
% 4.01/4.20 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 4.07/4.24 (Eq
% 4.07/4.24 (Exists fun D =>
% 4.07/4.24 And («$ki_exists_in_world_$i» a D)
% 4.07/4.24 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1))
% 4.07/4.24 True))
% 4.07/4.24 Clause #45 (by clausification #[44]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 4.07/4.24 (Eq
% 4.07/4.24 (And («$ki_exists_in_world_$i» a (skS.0 4 a a_1 a_2))
% 4.07/4.24 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 (skS.0 4 a a_1 a_2)) → defused W0 a_1))
% 4.07/4.24 True))
% 4.07/4.24 Clause #46 (by clausification #[45]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 4.07/4.24 (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)
% 4.07/4.24 True))
% 4.07/4.24 Clause #48 (by clausification #[46]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 4.07/4.24 (Eq («$ki_accessible» a a_2 → And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True))
% 4.07/4.24 Clause #49 (by clausification #[48]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 4.07/4.24 (Or (Eq («$ki_accessible» a a_2) False)
% 4.07/4.24 (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True)))
% 4.07/4.24 Clause #50 (by clausification #[49]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 4.07/4.24 (Or (Eq («$ki_accessible» a a_2) False)
% 4.07/4.24 (Or (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3))) False) (Eq (defused a_2 a_1) True))))
% 4.07/4.24 Clause #51 (by clausification #[50]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 4.07/4.24 (Or (Eq («$ki_accessible» a a_2) False)
% 4.07/4.24 (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)))))
% 4.07/4.24 Clause #52 (by forward demodulation #[51, 9]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq True False)
% 4.07/4.24 (Or (Eq («$ki_accessible» a a_1) False)
% 4.07/4.24 (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)))))
% 4.07/4.24 Clause #53 (by clausification #[52]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq («$ki_accessible» a a_1) False)
% 4.07/4.24 (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))))
% 4.07/4.24 Clause #55 (by superposition #[53, 7]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.07/4.24 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.07/4.24 (Or (Eq (defused a a_1) True)
% 4.07/4.24 (Or (Eq (bomb a a_1) False) (Or (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True))))
% 4.07/4.24 Clause #61 (by clausification #[38]): ∀ (a : «$ki_world») (a_1 : Iota),
% 4.07/4.24 Eq
% 4.07/4.24 (Not
% 4.07/4.24 («$ki_exists_in_world_$i» (skS.0 3 a) (skS.0 5 a a_1) →
% 4.07/4.24 Exists fun D =>
% 4.07/4.24 And («$ki_exists_in_world_$i» (skS.0 3 a) D)
% 4.07/4.24 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1))))
% 4.07/4.24 True
% 4.07/4.24 Clause #62 (by clausification #[61]): ∀ (a : «$ki_world») (a_1 : Iota),
% 4.07/4.24 Eq
% 4.07/4.24 («$ki_exists_in_world_$i» (skS.0 3 a) (skS.0 5 a a_1) →
% 4.07/4.24 Exists fun D =>
% 4.07/4.24 And («$ki_exists_in_world_$i» (skS.0 3 a) D)
% 4.07/4.24 (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)))
% 4.08/4.28 False
% 4.08/4.28 Clause #64 (by clausification #[62]): ∀ (a : «$ki_world») (a_1 : Iota),
% 4.08/4.28 Eq
% 4.08/4.28 (Exists fun D =>
% 4.08/4.28 And («$ki_exists_in_world_$i» (skS.0 3 a) D)
% 4.08/4.28 (And (bomb (skS.0 3 a) (skS.0 5 a a_1)) (h (skS.0 3 a) D) → defused (skS.0 3 a) (skS.0 5 a a_1)))
% 4.08/4.28 False
% 4.08/4.28 Clause #66 (by clausification #[55]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 4.08/4.28 (Or (Eq (defused a a_1) True) (Or (Eq (bomb a a_1) False) (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False)))
% 4.08/4.28 Clause #67 (by superposition #[66, 37]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq (defused (skS.0 3 a) a_1) True)
% 4.08/4.28 (Or (Eq (bomb (skS.0 3 a) a_1) False)
% 4.08/4.28 (Or (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True)))
% 4.08/4.28 Clause #73 (by clausification #[64]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Eq
% 4.08/4.28 (And («$ki_exists_in_world_$i» (skS.0 3 a) a_1)
% 4.08/4.28 (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)))
% 4.08/4.28 False
% 4.08/4.28 Clause #74 (by clausification #[73]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False)
% 4.08/4.28 (Eq (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1) → defused (skS.0 3 a) (skS.0 5 a a_2)) False)
% 4.08/4.28 Clause #75 (by clausification #[74]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False)
% 4.08/4.28 (Eq (And (bomb (skS.0 3 a) (skS.0 5 a a_2)) (h (skS.0 3 a) a_1)) True)
% 4.08/4.28 Clause #76 (by clausification #[74]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (defused (skS.0 3 a) (skS.0 5 a a_2)) False)
% 4.08/4.28 Clause #77 (by clausification #[75]): ∀ (a : «$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)
% 4.08/4.28 Clause #78 (by clausification #[75]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a) a_1) False) (Eq (bomb (skS.0 3 a) (skS.0 5 a a_2)) True)
% 4.08/4.28 Clause #79 (by forward demodulation #[77, 9]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (h (skS.0 3 a) a_1) True)
% 4.08/4.28 Clause #80 (by clausification #[79]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (h (skS.0 3 a) a_1) True
% 4.08/4.28 Clause #81 (by superposition #[78, 9]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (bomb (skS.0 3 a) (skS.0 5 a a_1)) True) (Eq False True)
% 4.08/4.28 Clause #82 (by clausification #[81]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (bomb (skS.0 3 a) (skS.0 5 a a_1)) True
% 4.08/4.28 Clause #84 (by superposition #[76, 9]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) False) (Eq False True)
% 4.08/4.28 Clause #85 (by clausification #[84]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) False
% 4.08/4.28 Clause #92 (by clausification #[67]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq (defused (skS.0 3 a) a_1) True)
% 4.08/4.28 (Or (Eq (bomb (skS.0 3 a) a_1) False) (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False))
% 4.08/4.28 Clause #94 (by superposition #[92, 82]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) True)
% 4.08/4.28 (Or (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) (Eq False True))
% 4.08/4.28 Clause #102 (by clausification #[94]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq (defused (skS.0 3 a) (skS.0 5 a a_1)) True)
% 4.08/4.28 (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False)
% 4.08/4.28 Clause #103 (by forward demodulation #[102, 85]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 4.08/4.28 Or (Eq False True) (Eq (h (skS.0 3 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False)
% 4.08/4.28 Clause #104 (by clausification #[103]): ∀ (a : «$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
% 4.08/4.28 Clause #105 (by superposition #[104, 80]): Eq False True
% 4.08/4.28 Clause #106 (by clausification #[105]): False
% 4.08/4.28 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------