TSTP Solution File: SYO890_16 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SYO890_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 3.79s 3.96s
% Output : Proof 3.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO890_16 : TPTP v8.2.0. Released v8.2.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n013.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 : Sat Aug 26 07:02:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.79/3.96 SZS status Theorem for theBenchmark.p
% 3.79/3.96 SZS output start Proof for theBenchmark.p
% 3.79/3.96 Clause #2 (by assumption #[]): Eq
% 3.79/3.96 (∀ (W V : «$ki_world») (X : Iota),
% 3.79/3.96 And («$ki_exists_in_world_$i» W X) («$ki_accessible» W V) → «$ki_exists_in_world_$i» V X)
% 3.79/3.96 True
% 3.79/3.96 Clause #4 (by assumption #[]): Eq
% 3.79/3.96 (Not
% 3.79/3.96 ((Exists fun X =>
% 3.79/3.96 And («$ki_exists_in_world_$i» «$ki_local_world» X)
% 3.79/3.96 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → And (e W X) (f W X))) →
% 3.79/3.96 ∀ (W : «$ki_world»),
% 3.79/3.96 «$ki_accessible» «$ki_local_world» W → Exists fun X => And («$ki_exists_in_world_$i» W X) (f W X)))
% 3.79/3.96 True
% 3.79/3.96 Clause #9 (by clausification #[2]): ∀ (a : «$ki_world»),
% 3.79/3.96 Eq
% 3.79/3.96 (∀ (V : «$ki_world») (X : Iota),
% 3.79/3.96 And («$ki_exists_in_world_$i» a X) («$ki_accessible» a V) → «$ki_exists_in_world_$i» V X)
% 3.79/3.96 True
% 3.79/3.96 Clause #10 (by clausification #[9]): ∀ (a a_1 : «$ki_world»),
% 3.79/3.96 Eq (∀ (X : Iota), And («$ki_exists_in_world_$i» a X) («$ki_accessible» a a_1) → «$ki_exists_in_world_$i» a_1 X) True
% 3.79/3.96 Clause #11 (by clausification #[10]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.79/3.96 Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2) → «$ki_exists_in_world_$i» a_2 a_1) True
% 3.79/3.96 Clause #12 (by clausification #[11]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.79/3.96 Or (Eq (And («$ki_exists_in_world_$i» a a_1) («$ki_accessible» a a_2)) False)
% 3.79/3.96 (Eq («$ki_exists_in_world_$i» a_2 a_1) True)
% 3.79/3.96 Clause #13 (by clausification #[12]): ∀ (a : «$ki_world») (a_1 : Iota) (a_2 : «$ki_world»),
% 3.79/3.96 Or (Eq («$ki_exists_in_world_$i» a a_1) True)
% 3.79/3.96 (Or (Eq («$ki_exists_in_world_$i» a_2 a_1) False) (Eq («$ki_accessible» a_2 a) False))
% 3.79/3.96 Clause #22 (by clausification #[4]): Eq
% 3.79/3.96 ((Exists fun X =>
% 3.79/3.96 And («$ki_exists_in_world_$i» «$ki_local_world» X)
% 3.79/3.96 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → And (e W X) (f W X))) →
% 3.79/3.96 ∀ (W : «$ki_world»),
% 3.79/3.96 «$ki_accessible» «$ki_local_world» W → Exists fun X => And («$ki_exists_in_world_$i» W X) (f W X))
% 3.79/3.96 False
% 3.79/3.96 Clause #23 (by clausification #[22]): Eq
% 3.79/3.96 (Exists fun X =>
% 3.79/3.96 And («$ki_exists_in_world_$i» «$ki_local_world» X)
% 3.79/3.96 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → And (e W X) (f W X)))
% 3.79/3.96 True
% 3.79/3.96 Clause #24 (by clausification #[22]): Eq
% 3.79/3.96 (∀ (W : «$ki_world»),
% 3.79/3.96 «$ki_accessible» «$ki_local_world» W → Exists fun X => And («$ki_exists_in_world_$i» W X) (f W X))
% 3.79/3.96 False
% 3.79/3.96 Clause #25 (by clausification #[23]): ∀ (a : Iota),
% 3.79/3.96 Eq
% 3.79/3.96 (And («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 1 a))
% 3.79/3.96 (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → And (e W (skS.0 1 a)) (f W (skS.0 1 a))))
% 3.79/3.96 True
% 3.79/3.96 Clause #26 (by clausification #[25]): ∀ (a : Iota),
% 3.79/3.96 Eq (∀ (W : «$ki_world»), «$ki_accessible» «$ki_local_world» W → And (e W (skS.0 1 a)) (f W (skS.0 1 a))) True
% 3.79/3.96 Clause #27 (by clausification #[25]): ∀ (a : Iota), Eq («$ki_exists_in_world_$i» «$ki_local_world» (skS.0 1 a)) True
% 3.79/3.96 Clause #28 (by clausification #[26]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.79/3.96 Eq («$ki_accessible» «$ki_local_world» a → And (e a (skS.0 1 a_1)) (f a (skS.0 1 a_1))) True
% 3.79/3.96 Clause #29 (by clausification #[28]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.79/3.96 Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (And (e a (skS.0 1 a_1)) (f a (skS.0 1 a_1))) True)
% 3.79/3.96 Clause #30 (by clausification #[29]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_accessible» «$ki_local_world» a) False) (Eq (f a (skS.0 1 a_1)) True)
% 3.79/3.96 Clause #33 (by superposition #[27, 13]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.79/3.96 Or (Eq («$ki_exists_in_world_$i» a (skS.0 1 a_1)) True)
% 3.79/3.96 (Or (Eq True False) (Eq («$ki_accessible» «$ki_local_world» a) False))
% 3.79/3.96 Clause #35 (by clausification #[24]): ∀ (a : «$ki_world»),
% 3.79/3.96 Eq
% 3.79/3.96 (Not
% 3.79/3.96 («$ki_accessible» «$ki_local_world» (skS.0 2 a) →
% 3.79/3.96 Exists fun X => And («$ki_exists_in_world_$i» (skS.0 2 a) X) (f (skS.0 2 a) X)))
% 3.79/3.96 True
% 3.79/3.96 Clause #36 (by clausification #[35]): ∀ (a : «$ki_world»),
% 3.79/3.97 Eq
% 3.79/3.97 («$ki_accessible» «$ki_local_world» (skS.0 2 a) →
% 3.79/3.97 Exists fun X => And («$ki_exists_in_world_$i» (skS.0 2 a) X) (f (skS.0 2 a) X))
% 3.79/3.97 False
% 3.79/3.97 Clause #37 (by clausification #[36]): ∀ (a : «$ki_world»), Eq («$ki_accessible» «$ki_local_world» (skS.0 2 a)) True
% 3.79/3.97 Clause #38 (by clausification #[36]): ∀ (a : «$ki_world»), Eq (Exists fun X => And («$ki_exists_in_world_$i» (skS.0 2 a) X) (f (skS.0 2 a) X)) False
% 3.79/3.97 Clause #39 (by superposition #[37, 30]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (f (skS.0 2 a) (skS.0 1 a_1)) True)
% 3.79/3.97 Clause #49 (by clausification #[33]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.79/3.97 Or (Eq («$ki_exists_in_world_$i» a (skS.0 1 a_1)) True) (Eq («$ki_accessible» «$ki_local_world» a) False)
% 3.79/3.97 Clause #50 (by superposition #[49, 37]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 1 a_1)) True) (Eq False True)
% 3.79/3.97 Clause #52 (by clausification #[38]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (And («$ki_exists_in_world_$i» (skS.0 2 a) a_1) (f (skS.0 2 a) a_1)) False
% 3.79/3.97 Clause #53 (by clausification #[52]): ∀ (a : «$ki_world») (a_1 : Iota),
% 3.79/3.97 Or (Eq («$ki_exists_in_world_$i» (skS.0 2 a) a_1) False) (Eq (f (skS.0 2 a) a_1) False)
% 3.79/3.97 Clause #56 (by clausification #[50]): ∀ (a : «$ki_world») (a_1 : Iota), Eq («$ki_exists_in_world_$i» (skS.0 2 a) (skS.0 1 a_1)) True
% 3.79/3.97 Clause #57 (by superposition #[56, 53]): ∀ (a : «$ki_world») (a_1 : Iota), Or (Eq True False) (Eq (f (skS.0 2 a) (skS.0 1 a_1)) False)
% 3.79/3.97 Clause #59 (by clausification #[57]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (f (skS.0 2 a) (skS.0 1 a_1)) False
% 3.79/3.97 Clause #60 (by clausification #[39]): ∀ (a : «$ki_world») (a_1 : Iota), Eq (f (skS.0 2 a) (skS.0 1 a_1)) True
% 3.79/3.97 Clause #61 (by superposition #[60, 59]): Eq True False
% 3.79/3.97 Clause #62 (by clausification #[61]): False
% 3.79/3.97 SZS output end Proof for theBenchmark.p
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