TSTP Solution File: SYO891_16 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n008.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 Sep 1 04:23:54 EDT 2023
% Result : Theorem 3.91s 4.09s
% Output : Proof 3.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n008.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 08:11:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.91/4.09 SZS status Theorem for theBenchmark.p
% 3.91/4.09 SZS output start Proof for theBenchmark.p
% 3.91/4.09 Clause #2 (by assumption #[]): Eq
% 3.91/4.09 (∀ (W V : «$ki_world») (X : Iota),
% 3.91/4.09 And («$ki_exists_in_world_$i» W X) («$ki_accessible» W V) → «$ki_exists_in_world_$i» V X)
% 3.91/4.09 True
% 3.91/4.09 Clause #8 (by assumption #[]): Eq
% 3.91/4.09 (Not
% 3.91/4.09 ((∀ (X : Iota),
% 3.91/4.09 «$ki_exists_in_world_$i» «$ki_local_world» X →
% 3.91/4.09 ∀ (W : «$ki_world»),
% 3.91/4.09 «$ki_accessible» «$ki_local_world» W → Exists fun Y => And («$ki_exists_in_world_$i» W Y) (qmltpeq W X Y)) →
% 3.91/4.09 (Exists fun X =>
% 3.91/4.09 And («$ki_exists_in_world_$i» «$ki_local_world» X)
% 3.91/4.09 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X))) →
% 3.91/4.09 Exists fun W =>
% 3.91/4.09 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X))))
% 3.91/4.09 True
% 3.91/4.09 Clause #16 (by clausification #[2]): ∀ (a : «$ki_world»),
% 3.91/4.09 Eq
% 3.91/4.09 (∀ (V : «$ki_world») (X : Iota),
% 3.91/4.09 And («$ki_exists_in_world_$i» a X) («$ki_accessible» a V) → «$ki_exists_in_world_$i» V X)
% 3.91/4.09 True
% 3.91/4.09 Clause #17 (by clausification #[16]): ∀ (a a_1 : «$ki_world»),
% 3.91/4.09 Eq (∀ (X : Iota), And («$ki_exists_in_world_$i» a X) («$ki_accessible» a a_1) → «$ki_exists_in_world_$i» a_1 X) True
% 3.91/4.09 Clause #18 (by clausification #[17]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.91/4.09 Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2) → «$ki_exists_in_world_$i» a_2 a_1) True
% 3.91/4.09 Clause #19 (by clausification #[18]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.91/4.09 Or (Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2)) False)
% 3.91/4.09 (Eq («$ki_exists_in_world_$i» a_2 a_1) True)
% 3.91/4.09 Clause #20 (by clausification #[19]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.91/4.09 Or (Eq («$ki_exists_in_world_$i» a a_1) True)
% 3.91/4.09 (Or (Eq («$ki_exists_in_world_$i» a_2 a_1) False) (Eq («$ki_accessible» a_2 a) False))
% 3.91/4.09 Clause #53 (by clausification #[8]): Eq
% 3.91/4.09 ((∀ (X : Iota),
% 3.91/4.09 «$ki_exists_in_world_$i» «$ki_local_world» X →
% 3.91/4.09 ∀ (W : «$ki_world»),
% 3.91/4.09 «$ki_accessible» «$ki_local_world» W → Exists fun Y => And («$ki_exists_in_world_$i» W Y) (qmltpeq W X Y)) →
% 3.91/4.09 (Exists fun X =>
% 3.91/4.09 And («$ki_exists_in_world_$i» «$ki_local_world» X)
% 3.91/4.09 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X))) →
% 3.91/4.09 Exists fun W =>
% 3.91/4.09 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X)))
% 3.91/4.09 False
% 3.91/4.09 Clause #55 (by clausification #[53]): Eq
% 3.91/4.09 ((Exists fun X =>
% 3.91/4.09 And («$ki_exists_in_world_$i» «$ki_local_world» X)
% 3.91/4.09 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X))) →
% 3.91/4.09 Exists fun W =>
% 3.91/4.09 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X)))
% 3.91/4.09 False
% 3.91/4.09 Clause #64 (by clausification #[55]): Eq
% 3.91/4.09 (Exists fun X =>
% 3.91/4.09 And («$ki_exists_in_world_$i» «$ki_local_world» X)
% 3.91/4.09 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W X)))
% 3.91/4.09 True
% 3.91/4.09 Clause #65 (by clausification #[55]): Eq
% 3.91/4.09 (Exists fun W =>
% 3.91/4.09 And («$ki_accessible» «$ki_local_world» W) (Exists fun X => And («$ki_exists_in_world_$i» W X) (p W X)))
% 3.91/4.09 False
% 3.91/4.09 Clause #66 (by clausification #[64]): ∀ (a : Iota),
% 3.91/4.09 Eq
% 3.91/4.09 (And («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 2 a))
% 3.91/4.09 (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W (skS.0 2 a))))
% 3.91/4.09 True
% 3.91/4.09 Clause #67 (by clausification #[66]): ∀ (a : Iota), Eq (Exists fun W => And («$ki_accessible» «$ki_local_world» W) (p W (skS.0 2 a))) True
% 3.91/4.09 Clause #68 (by clausification #[66]): ∀ (a : Iota), Eq («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 2 a)) True
% 3.91/4.09 Clause #69 (by clausification #[67]): ∀ (a : Iota) (a_1 : «$ki_world»),
% 3.91/4.09 Eq (And («$ki_accessible» «$ki_local_world» (skS.0 3 a a_1)) (p (skS.0 3 a a_1) (skS.0 2 a))) True
% 3.91/4.09 Clause #70 (by clausification #[69]): ∀ (a : Iota) (a_1 : «$ki_world»), Eq (p (skS.0 3 a a_1) (skS.0 2 a)) True
% 3.91/4.10 Clause #71 (by clausification #[69]): ∀ (a : Iota) (a_1 : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 3 a a_1)) True
% 3.91/4.10 Clause #77 (by superposition #[68, 20]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.91/4.10 Or (Eq («$ki_exists_in_world_$i» a (skS.0 2 a_1)) True)
% 3.91/4.10 (Or (Eq True False) (Eq («$ki_accessible» «$ki_local_world» a) False))
% 3.91/4.10 Clause #80 (by clausification #[77]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.91/4.10 Or (Eq («$ki_exists_in_world_$i» a (skS.0 2 a_1)) True) (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.91/4.10 Clause #81 (by superposition #[80, 71]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota),
% 3.91/4.10 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a a_1) (skS.0 2 a_2)) True) (Eq False True)
% 3.91/4.10 Clause #87 (by clausification #[81]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), Eq («$ki_exists_in_world_$i» (skS.0 3 a a_1) (skS.0 2 a_2)) True
% 3.91/4.10 Clause #89 (by clausification #[65]): ∀ (a : «$ki_world»),
% 3.91/4.10 Eq (And («$ki_accessible» «$ki_local_world» a) (Exists fun X => And («$ki_exists_in_world_$i» a X) (p a X))) False
% 3.91/4.10 Clause #90 (by clausification #[89]): ∀ (a : «$ki_world»),
% 3.91/4.10 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.91/4.10 (Eq (Exists fun X => And («$ki_exists_in_world_$i» a X) (p a X)) False)
% 3.91/4.10 Clause #91 (by clausification #[90]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.91/4.10 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (And («$ki_exists_in_world_$i» a a_1) (p a a_1)) False)
% 3.91/4.10 Clause #92 (by clausification #[91]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.91/4.10 Or (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.91/4.10 (Or (Eq («$ki_exists_in_world_$i» a a_1) False) (Eq (p a a_1) False))
% 3.91/4.10 Clause #93 (by superposition #[92, 71]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota),
% 3.91/4.10 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))
% 3.91/4.10 Clause #110 (by clausification #[93]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota),
% 3.91/4.10 Or (Eq («$ki_exists_in_world_$i» (skS.0 3 a a_1) a_2) False) (Eq (p (skS.0 3 a a_1) a_2) False)
% 3.91/4.10 Clause #111 (by superposition #[110, 87]): ∀ (a : Iota) (a_1 : «$ki_world») (a_2 : Iota), Or (Eq (p (skS.0 3 a a_1) (skS.0 2 a_2)) False) (Eq False True)
% 3.91/4.10 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
% 3.91/4.10 Clause #115 (by superposition #[114, 70]): Eq False True
% 3.91/4.10 Clause #116 (by clausification #[115]): False
% 3.91/4.10 SZS output end Proof for theBenchmark.p
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