TSTP Solution File: PLA053_4 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 3.62s 3.80s
% Output : Proof 3.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PLA053_4 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 05:31:34 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.62/3.80 SZS status Theorem for theBenchmark.p
% 3.62/3.80 SZS output start Proof for theBenchmark.p
% 3.62/3.80 Clause #0 (by assumption #[]): Eq (∀ (W : «$ki_world»), «$ki_accessible» W W) True
% 3.62/3.80 Clause #2 (by assumption #[]): Eq (∀ (W : «$ki_world») (X : Iota), «$ki_exists_in_world_$i» W X) True
% 3.62/3.80 Clause #6 (by assumption #[]): Eq
% 3.62/3.80 (∀ (W : «$ki_world»),
% 3.62/3.80 «$ki_accessible» «$ki_local_world» W →
% 3.62/3.80 ∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» W X →
% 3.62/3.80 Exists fun D =>
% 3.62/3.80 And («$ki_exists_in_world_$i» W D)
% 3.62/3.80 (∀ (W0 : «$ki_world»), «$ki_accessible» W W0 → And (bomb W0 X) (h W0 D) → defused W0 X))
% 3.62/3.80 True
% 3.62/3.80 Clause #7 (by assumption #[]): Eq
% 3.62/3.80 (Not
% 3.62/3.80 (∀ (W : «$ki_world»),
% 3.62/3.80 «$ki_accessible» «$ki_local_world» W →
% 3.62/3.80 ∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» W X →
% 3.62/3.80 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X)))
% 3.62/3.80 True
% 3.62/3.80 Clause #8 (by clausification #[0]): ∀ (a : «$ki_world»), Eq («$ki_accessible» a a) True
% 3.62/3.80 Clause #9 (by clausification #[2]): ∀ (a : «$ki_world»), Eq (∀ (X : Iota), «$ki_exists_in_world_$i» a X) True
% 3.62/3.80 Clause #10 (by clausification #[9]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» a a_1) True
% 3.62/3.80 Clause #28 (by clausification #[7]): Eq
% 3.62/3.80 (∀ (W : «$ki_world»),
% 3.62/3.80 «$ki_accessible» «$ki_local_world» W →
% 3.62/3.80 ∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» W X →
% 3.62/3.80 Exists fun D => And («$ki_exists_in_world_$i» W D) (And (bomb W X) (h W D) → defused W X))
% 3.62/3.80 False
% 3.62/3.80 Clause #29 (by clausification #[28]): ∀ (a : «$ki_world»),
% 3.62/3.80 Eq
% 3.62/3.80 (Not
% 3.62/3.80 («$ki_accessible» «$ki_local_world» (skS.0 2 a) →
% 3.62/3.80 ∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» (skS.0 2 a) X →
% 3.62/3.80 Exists fun D =>
% 3.62/3.80 And («$ki_exists_in_world_$i» (skS.0 2 a) D)
% 3.62/3.80 (And (bomb (skS.0 2 a) X) (h (skS.0 2 a) D) → defused (skS.0 2 a) X)))
% 3.62/3.80 True
% 3.62/3.80 Clause #30 (by clausification #[29]): ∀ (a : «$ki_world»),
% 3.62/3.80 Eq
% 3.62/3.80 («$ki_accessible» «$ki_local_world» (skS.0 2 a) →
% 3.62/3.80 ∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» (skS.0 2 a) X →
% 3.62/3.80 Exists fun D =>
% 3.62/3.80 And («$ki_exists_in_world_$i» (skS.0 2 a) D)
% 3.62/3.80 (And (bomb (skS.0 2 a) X) (h (skS.0 2 a) D) → defused (skS.0 2 a) X))
% 3.62/3.80 False
% 3.62/3.80 Clause #31 (by clausification #[30]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 2 a)) True
% 3.62/3.80 Clause #32 (by clausification #[30]): ∀ (a : «$ki_world»),
% 3.62/3.80 Eq
% 3.62/3.80 (∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» (skS.0 2 a) X →
% 3.62/3.80 Exists fun D =>
% 3.62/3.80 And («$ki_exists_in_world_$i» (skS.0 2 a) D)
% 3.62/3.80 (And (bomb (skS.0 2 a) X) (h (skS.0 2 a) D) → defused (skS.0 2 a) X))
% 3.62/3.80 False
% 3.62/3.80 Clause #52 (by clausification #[6]): ∀ (a : «$ki_world»),
% 3.62/3.80 Eq
% 3.62/3.80 («$ki_accessible» «$ki_local_world» a →
% 3.62/3.80 ∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» a X →
% 3.62/3.80 Exists fun D =>
% 3.62/3.80 And («$ki_exists_in_world_$i» a D)
% 3.62/3.80 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X))
% 3.62/3.80 True
% 3.62/3.80 Clause #53 (by clausification #[52]): ∀ (a : «$ki_world»),
% 3.62/3.80 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.80 (Eq
% 3.62/3.80 (∀ (X : Iota),
% 3.62/3.80 «$ki_exists_in_world_$i» a X →
% 3.62/3.80 Exists fun D =>
% 3.62/3.80 And («$ki_exists_in_world_$i» a D)
% 3.62/3.80 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 X) (h W0 D) → defused W0 X))
% 3.62/3.80 True)
% 3.62/3.80 Clause #54 (by clausification #[53]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.62/3.80 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.80 (Eq
% 3.62/3.80 («$ki_exists_in_world_$i» a a_1 →
% 3.62/3.80 Exists fun D =>
% 3.62/3.80 And («$ki_exists_in_world_$i» a D)
% 3.62/3.80 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1))
% 3.62/3.80 True)
% 3.62/3.80 Clause #55 (by clausification #[54]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.62/3.80 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 3.62/3.82 (Eq
% 3.62/3.82 (Exists fun D =>
% 3.62/3.82 And («$ki_exists_in_world_$i» a D)
% 3.62/3.82 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 D) → defused W0 a_1))
% 3.62/3.82 True))
% 3.62/3.82 Clause #56 (by clausification #[55]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 3.62/3.82 (Eq
% 3.62/3.82 (And («$ki_exists_in_world_$i» a (skS.0 4 a a_1 a_2))
% 3.62/3.82 (∀ (W0 : «$ki_world»), «$ki_accessible» a W0 → And (bomb W0 a_1) (h W0 (skS.0 4 a a_1 a_2)) → defused W0 a_1))
% 3.62/3.82 True))
% 3.62/3.82 Clause #57 (by clausification #[56]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 3.62/3.82 (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)
% 3.62/3.82 True))
% 3.62/3.82 Clause #59 (by clausification #[57]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 3.62/3.82 (Eq («$ki_accessible» a a_2 → And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True))
% 3.62/3.82 Clause #60 (by clausification #[59]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 3.62/3.82 (Or (Eq («$ki_accessible» a a_2) False)
% 3.62/3.82 (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3)) → defused a_2 a_1) True)))
% 3.62/3.82 Clause #61 (by clausification #[60]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 3.62/3.82 (Or (Eq («$ki_accessible» a a_2) False)
% 3.62/3.82 (Or (Eq (And (bomb a_2 a_1) (h a_2 (skS.0 4 a a_1 a_3))) False) (Eq (defused a_2 a_1) True))))
% 3.62/3.82 Clause #62 (by clausification #[61]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world») (a_3 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_exists_in_world_$i» a a_1) False)
% 3.62/3.82 (Or (Eq («$ki_accessible» a a_2) False)
% 3.62/3.82 (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)))))
% 3.62/3.82 Clause #63 (by forward demodulation #[62, 10]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq True False)
% 3.62/3.82 (Or (Eq («$ki_accessible» a a_1) False)
% 3.62/3.82 (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)))))
% 3.62/3.82 Clause #64 (by clausification #[63]): ∀ (a a_1 : «$ki_world») (a_2 a_3 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq («$ki_accessible» a a_1) False)
% 3.62/3.82 (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))))
% 3.62/3.82 Clause #66 (by superposition #[64, 8]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.82 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.82 (Or (Eq (defused a a_1) True)
% 3.62/3.82 (Or (Eq (bomb a a_1) False) (Or (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True))))
% 3.62/3.82 Clause #72 (by clausification #[32]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.62/3.82 Eq
% 3.62/3.82 (Not
% 3.62/3.82 («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 5 a a_1) →
% 3.62/3.82 Exists fun D =>
% 3.62/3.82 And («$ki_exists_in_world_$i» (skS.0 2 a) D)
% 3.62/3.82 (And (bomb (skS.0 2 a) (skS.0 5 a a_1)) (h (skS.0 2 a) D) → defused (skS.0 2 a) (skS.0 5 a a_1))))
% 3.62/3.82 True
% 3.62/3.82 Clause #73 (by clausification #[72]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.62/3.82 Eq
% 3.62/3.82 («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 5 a a_1) →
% 3.62/3.82 Exists fun D =>
% 3.62/3.82 And («$ki_exists_in_world_$i» (skS.0 2 a) D)
% 3.62/3.82 (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)))
% 3.62/3.84 False
% 3.62/3.84 Clause #75 (by clausification #[73]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.62/3.84 Eq
% 3.62/3.84 (Exists fun D =>
% 3.62/3.84 And («$ki_exists_in_world_$i» (skS.0 2 a) D)
% 3.62/3.84 (And (bomb (skS.0 2 a) (skS.0 5 a a_1)) (h (skS.0 2 a) D) → defused (skS.0 2 a) (skS.0 5 a a_1)))
% 3.62/3.84 False
% 3.62/3.84 Clause #77 (by clausification #[66]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.62/3.84 (Or (Eq (defused a a_1) True) (Or (Eq (bomb a a_1) False) (Eq (h a (skS.0 4 «$ki_local_world» a_1 a_2)) False)))
% 3.62/3.84 Clause #78 (by superposition #[77, 31]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq (defused (skS.0 2 a) a_1) True)
% 3.62/3.84 (Or (Eq (bomb (skS.0 2 a) a_1) False)
% 3.62/3.84 (Or (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False) (Eq False True)))
% 3.62/3.84 Clause #82 (by clausification #[75]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Eq
% 3.62/3.84 (And («$ki_exists_in_world_$i» (skS.0 2 a) a_1)
% 3.62/3.84 (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)))
% 3.62/3.84 False
% 3.62/3.84 Clause #83 (by clausification #[82]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False)
% 3.62/3.84 (Eq (And (bomb (skS.0 2 a) (skS.0 5 a a_2)) (h (skS.0 2 a) a_1) → defused (skS.0 2 a) (skS.0 5 a a_2)) False)
% 3.62/3.84 Clause #84 (by clausification #[83]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False)
% 3.62/3.84 (Eq (And (bomb (skS.0 2 a) (skS.0 5 a a_2)) (h (skS.0 2 a) a_1)) True)
% 3.62/3.84 Clause #85 (by clausification #[83]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) (Eq (defused (skS.0 2 a) (skS.0 5 a a_2)) False)
% 3.62/3.84 Clause #86 (by clausification #[84]): ∀ (a : «$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)
% 3.62/3.84 Clause #87 (by clausification #[84]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) (Eq (bomb (skS.0 2 a) (skS.0 5 a a_2)) True)
% 3.62/3.84 Clause #88 (by forward demodulation #[86, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (h (skS.0 2 a) a_1) True)
% 3.62/3.84 Clause #89 (by clausification #[88]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (h (skS.0 2 a) a_1) True
% 3.62/3.84 Clause #90 (by superposition #[87, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (bomb (skS.0 2 a) (skS.0 5 a a_1)) True) (Eq False True)
% 3.62/3.84 Clause #93 (by clausification #[90]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (bomb (skS.0 2 a) (skS.0 5 a a_1)) True
% 3.62/3.84 Clause #95 (by superposition #[85, 10]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) False) (Eq False True)
% 3.62/3.84 Clause #96 (by clausification #[95]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) False
% 3.62/3.84 Clause #103 (by clausification #[78]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq (defused (skS.0 2 a) a_1) True)
% 3.62/3.84 (Or (Eq (bomb (skS.0 2 a) a_1) False) (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» a_1 a_2)) False))
% 3.62/3.84 Clause #105 (by superposition #[103, 93]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) True)
% 3.62/3.84 (Or (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False) (Eq False True))
% 3.62/3.84 Clause #113 (by clausification #[105]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq (defused (skS.0 2 a) (skS.0 5 a a_1)) True)
% 3.62/3.84 (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False)
% 3.62/3.84 Clause #114 (by forward demodulation #[113, 96]): ∀ (a : «$ki_world») (a_1 a_2 : Iota),
% 3.62/3.84 Or (Eq False True) (Eq (h (skS.0 2 a) (skS.0 4 «$ki_local_world» (skS.0 5 a a_1) a_2)) False)
% 3.62/3.84 Clause #115 (by clausification #[114]): ∀ (a : «$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
% 3.62/3.84 Clause #116 (by superposition #[115, 89]): Eq False True
% 3.62/3.84 Clause #117 (by clausification #[116]): False
% 3.62/3.84 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------