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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : PUZ149_13 : TPTP v9.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n028.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 07:58:26 PM UTC 2025

% Result   : Theorem 4.66s 4.86s
% Output   : Proof 4.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : PUZ149_13 : TPTP v9.2.0. Released v8.2.0.
% 0.12/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n028.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Oct  2 20:56:23 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 4.66/4.86  SZS status Theorem for theBenchmark.p
% 4.66/4.86  SZS output start Proof for theBenchmark.p
% 4.66/4.86  Clause #1 (by assumption #[]): Eq
% 4.66/4.86    ((∀ (W : «$ki_world»),
% 4.66/4.86        «$ki_accessible» #idx(pour_a) «$ki_local_world» W →
% 4.66/4.86          ∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) W W0 → Not (acid W0)) →
% 4.66/4.86      ∀ (W : «$ki_world»), «$ki_accessible» #idx(make_c) «$ki_local_world» W → Not (acid W))
% 4.66/4.86    True
% 4.66/4.86  Clause #4 (by assumption #[]): Eq (∀ (W : «$ki_world»), «$ki_accessible» #idx(pour_a) «$ki_local_world» W → Not (acid W)) True
% 4.66/4.86  Clause #5 (by assumption #[]): Eq (Exists fun W => And («$ki_accessible» #idx(make_c) «$ki_local_world» W) (acid W)) True
% 4.66/4.86  Clause #6 (by assumption #[]): Eq
% 4.66/4.86    (Not
% 4.66/4.86      (And (Exists fun W => And («$ki_accessible» #idx(pour_a) «$ki_local_world» W) (Not (acid W)))
% 4.66/4.86        (Exists fun W =>
% 4.66/4.86          And («$ki_accessible» #idx(pour_a) «$ki_local_world» W)
% 4.66/4.86            (Exists fun W0 => And («$ki_accessible» #idx(pour_b) W W0) (acid W0)))))
% 4.66/4.86    True
% 4.66/4.86  Clause #7 (by clausification #[4]): ∀ (a : «$ki_world»), Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a → Not (acid a)) True
% 4.66/4.86  Clause #8 (by clausification #[7]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False) (Eq (Not (acid a)) True)
% 4.66/4.86  Clause #9 (by clausification #[8]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False) (Eq (acid a) False)
% 4.66/4.86  Clause #24 (by clausification #[1]): Or
% 4.66/4.86    (Eq
% 4.66/4.86      (∀ (W : «$ki_world»),
% 4.66/4.86        «$ki_accessible» #idx(pour_a) «$ki_local_world» W →
% 4.66/4.86          ∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) W W0 → Not (acid W0))
% 4.66/4.86      False)
% 4.66/4.86    (Eq (∀ (W : «$ki_world»), «$ki_accessible» #idx(make_c) «$ki_local_world» W → Not (acid W)) True)
% 4.66/4.86  Clause #25 (by clausification #[24]): ∀ (a : «$ki_world»),
% 4.66/4.86    Or (Eq (∀ (W : «$ki_world»), «$ki_accessible» #idx(make_c) «$ki_local_world» W → Not (acid W)) True)
% 4.66/4.86      (Eq
% 4.66/4.86        (Not
% 4.66/4.86          («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a) →
% 4.66/4.86            ∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) (skS.0 2 a) W0 → Not (acid W0)))
% 4.66/4.86        True)
% 4.66/4.86  Clause #26 (by clausification #[25]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.86    Or
% 4.66/4.86      (Eq
% 4.66/4.86        (Not
% 4.66/4.86          («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a) →
% 4.66/4.86            ∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) (skS.0 2 a) W0 → Not (acid W0)))
% 4.66/4.86        True)
% 4.66/4.86      (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a_1 → Not (acid a_1)) True)
% 4.66/4.86  Clause #27 (by clausification #[26]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.86    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a → Not (acid a)) True)
% 4.66/4.86      (Eq
% 4.66/4.86        («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a_1) →
% 4.66/4.86          ∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) (skS.0 2 a_1) W0 → Not (acid W0))
% 4.66/4.86        False)
% 4.66/4.86  Clause #28 (by clausification #[27]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.86    Or
% 4.66/4.86      (Eq
% 4.66/4.86        («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a) →
% 4.66/4.86          ∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) (skS.0 2 a) W0 → Not (acid W0))
% 4.66/4.86        False)
% 4.66/4.86      (Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a_1) False) (Eq (Not (acid a_1)) True))
% 4.66/4.86  Clause #29 (by clausification #[28]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.86    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.86      (Or (Eq (Not (acid a)) True) (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a_1)) True))
% 4.66/4.86  Clause #30 (by clausification #[28]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.86    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.86      (Or (Eq (Not (acid a)) True)
% 4.66/4.86        (Eq (∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) (skS.0 2 a_1) W0 → Not (acid W0)) False))
% 4.66/4.86  Clause #31 (by clausification #[29]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.86    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.86      (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a_1)) True) (Eq (acid a) False))
% 4.66/4.86  Clause #40 (by clausification #[5]): ∀ (a : «$ki_world»), Eq (And («$ki_accessible» #idx(make_c) «$ki_local_world» (skS.0 4 a)) (acid (skS.0 4 a))) True
% 4.66/4.88  Clause #41 (by clausification #[40]): ∀ (a : «$ki_world»), Eq (acid (skS.0 4 a)) True
% 4.66/4.88  Clause #42 (by clausification #[40]): ∀ (a : «$ki_world»), Eq («$ki_accessible» #idx(make_c) «$ki_local_world» (skS.0 4 a)) True
% 4.66/4.88  Clause #45 (by superposition #[42, 31]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.88    Or (Eq True False)
% 4.66/4.88      (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a)) True) (Eq (acid (skS.0 4 a_1)) False))
% 4.66/4.88  Clause #63 (by clausification #[30]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.88    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.88      (Or (Eq (∀ (W0 : «$ki_world»), «$ki_accessible» #idx(pour_b) (skS.0 2 a_1) W0 → Not (acid W0)) False)
% 4.66/4.88        (Eq (acid a) False))
% 4.66/4.88  Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.88    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.88      (Or (Eq (acid a) False)
% 4.66/4.88        (Eq (Not («$ki_accessible» #idx(pour_b) (skS.0 2 a_1) (skS.0 8 a_1 a_2) → Not (acid (skS.0 8 a_1 a_2)))) True))
% 4.66/4.88  Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.88    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.88      (Or (Eq (acid a) False)
% 4.66/4.88        (Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a_1) (skS.0 8 a_1 a_2) → Not (acid (skS.0 8 a_1 a_2))) False))
% 4.66/4.88  Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.88    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.88      (Or (Eq (acid a) False) (Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a_1) (skS.0 8 a_1 a_2)) True))
% 4.66/4.88  Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.88    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.88      (Or (Eq (acid a) False) (Eq (Not (acid (skS.0 8 a_1 a_2))) False))
% 4.66/4.88  Clause #68 (by superposition #[66, 42]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.88    Or (Eq (acid (skS.0 4 a)) False)
% 4.66/4.88      (Or (Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a_1) (skS.0 8 a_1 a_2)) True) (Eq False True))
% 4.66/4.88  Clause #69 (by clausification #[6]): Eq
% 4.66/4.88    (And (Exists fun W => And («$ki_accessible» #idx(pour_a) «$ki_local_world» W) (Not (acid W)))
% 4.66/4.88      (Exists fun W =>
% 4.66/4.88        And («$ki_accessible» #idx(pour_a) «$ki_local_world» W)
% 4.66/4.88          (Exists fun W0 => And («$ki_accessible» #idx(pour_b) W W0) (acid W0))))
% 4.66/4.88    False
% 4.66/4.88  Clause #70 (by clausification #[69]): Or (Eq (Exists fun W => And («$ki_accessible» #idx(pour_a) «$ki_local_world» W) (Not (acid W))) False)
% 4.66/4.88    (Eq
% 4.66/4.88      (Exists fun W =>
% 4.66/4.88        And («$ki_accessible» #idx(pour_a) «$ki_local_world» W)
% 4.66/4.88          (Exists fun W0 => And («$ki_accessible» #idx(pour_b) W W0) (acid W0)))
% 4.66/4.88      False)
% 4.66/4.88  Clause #71 (by clausification #[70]): ∀ (a : «$ki_world»),
% 4.66/4.88    Or
% 4.66/4.88      (Eq
% 4.66/4.88        (Exists fun W =>
% 4.66/4.88          And («$ki_accessible» #idx(pour_a) «$ki_local_world» W)
% 4.66/4.88            (Exists fun W0 => And («$ki_accessible» #idx(pour_b) W W0) (acid W0)))
% 4.66/4.88        False)
% 4.66/4.88      (Eq (And («$ki_accessible» #idx(pour_a) «$ki_local_world» a) (Not (acid a))) False)
% 4.66/4.88  Clause #72 (by clausification #[71]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.88    Or (Eq (And («$ki_accessible» #idx(pour_a) «$ki_local_world» a) (Not (acid a))) False)
% 4.66/4.88      (Eq
% 4.66/4.88        (And («$ki_accessible» #idx(pour_a) «$ki_local_world» a_1)
% 4.66/4.88          (Exists fun W0 => And («$ki_accessible» #idx(pour_b) a_1 W0) (acid W0)))
% 4.66/4.88        False)
% 4.66/4.88  Clause #73 (by clausification #[72]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.88    Or
% 4.66/4.88      (Eq
% 4.66/4.88        (And («$ki_accessible» #idx(pour_a) «$ki_local_world» a)
% 4.66/4.88          (Exists fun W0 => And («$ki_accessible» #idx(pour_b) a W0) (acid W0)))
% 4.66/4.88        False)
% 4.66/4.88      (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a_1) False) (Eq (Not (acid a_1)) False))
% 4.66/4.88  Clause #74 (by clausification #[73]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.88    Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False)
% 4.66/4.88      (Or (Eq (Not (acid a)) False)
% 4.66/4.88        (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a_1) False)
% 4.66/4.88          (Eq (Exists fun W0 => And («$ki_accessible» #idx(pour_b) a_1 W0) (acid W0)) False)))
% 4.66/4.91  Clause #75 (by clausification #[74]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.91    Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False)
% 4.66/4.91      (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a_1) False)
% 4.66/4.91        (Or (Eq (Exists fun W0 => And («$ki_accessible» #idx(pour_b) a_1 W0) (acid W0)) False) (Eq (acid a) True)))
% 4.66/4.91  Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False)
% 4.66/4.91      (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a_1) False)
% 4.66/4.91        (Or (Eq (acid a) True) (Eq (And («$ki_accessible» #idx(pour_b) a_1 a_2) (acid a_2)) False)))
% 4.66/4.91  Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False)
% 4.66/4.91      (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a_1) False)
% 4.66/4.91        (Or (Eq (acid a) True) (Or (Eq («$ki_accessible» #idx(pour_b) a_1 a_2) False) (Eq (acid a_2) False))))
% 4.66/4.91  Clause #82 (by clausification #[67]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq («$ki_accessible» #idx(make_c) «$ki_local_world» a) False)
% 4.66/4.91      (Or (Eq (acid a) False) (Eq (acid (skS.0 8 a_1 a_2)) True))
% 4.66/4.91  Clause #83 (by superposition #[82, 42]): ∀ (a a_1 a_2 : «$ki_world»), Or (Eq (acid (skS.0 4 a)) False) (Or (Eq (acid (skS.0 8 a_1 a_2)) True) (Eq False True))
% 4.66/4.91  Clause #86 (by clausification #[83]): ∀ (a a_1 a_2 : «$ki_world»), Or (Eq (acid (skS.0 4 a)) False) (Eq (acid (skS.0 8 a_1 a_2)) True)
% 4.66/4.91  Clause #87 (by superposition #[86, 41]): ∀ (a a_1 : «$ki_world»), Or (Eq (acid (skS.0 8 a a_1)) True) (Eq False True)
% 4.66/4.91  Clause #88 (by clausification #[87]): ∀ (a a_1 : «$ki_world»), Eq (acid (skS.0 8 a a_1)) True
% 4.66/4.91  Clause #89 (by clausification #[45]): ∀ (a a_1 : «$ki_world»),
% 4.66/4.91    Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a)) True) (Eq (acid (skS.0 4 a_1)) False)
% 4.66/4.91  Clause #90 (by superposition #[89, 41]): ∀ (a : «$ki_world»), Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a)) True) (Eq False True)
% 4.66/4.91  Clause #91 (by clausification #[90]): ∀ (a : «$ki_world»), Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» (skS.0 2 a)) True
% 4.66/4.91  Clause #92 (by superposition #[91, 9]): ∀ (a : «$ki_world»), Or (Eq True False) (Eq (acid (skS.0 2 a)) False)
% 4.66/4.91  Clause #93 (by superposition #[91, 77]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq True False)
% 4.66/4.91      (Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False)
% 4.66/4.91        (Or (Eq (acid (skS.0 2 a_1)) True) (Or (Eq («$ki_accessible» #idx(pour_b) a a_2) False) (Eq (acid a_2) False))))
% 4.66/4.91  Clause #94 (by clausification #[92]): ∀ (a : «$ki_world»), Eq (acid (skS.0 2 a)) False
% 4.66/4.91  Clause #104 (by clausification #[93]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq («$ki_accessible» #idx(pour_a) «$ki_local_world» a) False)
% 4.66/4.91      (Or (Eq (acid (skS.0 2 a_1)) True) (Or (Eq («$ki_accessible» #idx(pour_b) a a_2) False) (Eq (acid a_2) False)))
% 4.66/4.91  Clause #105 (by superposition #[104, 91]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq (acid (skS.0 2 a)) True)
% 4.66/4.91      (Or (Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a_1) a_2) False) (Or (Eq (acid a_2) False) (Eq False True)))
% 4.66/4.91  Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq (acid (skS.0 2 a)) True)
% 4.66/4.91      (Or (Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a_1) a_2) False) (Eq (acid a_2) False))
% 4.66/4.91  Clause #110 (by clausification #[68]): ∀ (a a_1 a_2 : «$ki_world»),
% 4.66/4.91    Or (Eq (acid (skS.0 4 a)) False) (Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a_1) (skS.0 8 a_1 a_2)) True)
% 4.66/4.91  Clause #111 (by superposition #[110, 41]): ∀ (a a_1 : «$ki_world»), Or (Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a) (skS.0 8 a a_1)) True) (Eq False True)
% 4.66/4.91  Clause #113 (by clausification #[111]): ∀ (a a_1 : «$ki_world»), Eq («$ki_accessible» #idx(pour_b) (skS.0 2 a) (skS.0 8 a a_1)) True
% 4.66/4.91  Clause #114 (by superposition #[113, 106]): ∀ (a a_1 a_2 : «$ki_world»), Or (Eq (acid (skS.0 2 a)) True) (Or (Eq True False) (Eq (acid (skS.0 8 a_1 a_2)) False))
% 4.66/4.91  Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : «$ki_world»), Or (Eq (acid (skS.0 2 a)) True) (Eq (acid (skS.0 8 a_1 a_2)) False)
% 4.66/4.91  Clause #116 (by superposition #[115, 88]): ∀ (a : «$ki_world»), Or (Eq (acid (skS.0 2 a)) True) (Eq False True)
% 4.66/4.91  Clause #117 (by clausification #[116]): ∀ (a : «$ki_world»), Eq (acid (skS.0 2 a)) True
% 4.66/4.91  Clause #118 (by superposition #[117, 94]): Eq True False
% 4.66/4.91  Clause #119 (by clausification #[118]): False
% 4.66/4.91  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------