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Duper---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : Duper---1.0
% Problem  : NUM533+1 : TPTP v9.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : duper %s

% Computer : n004.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 07:56:40 PM UTC 2025

% Result   : Theorem 4.22s 4.39s
% Output   : Proof 4.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM533+1 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.13  % Command    : duper %s
% 0.13/0.34  % Computer : n004.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   : Fri Oct  3 08:40:38 EDT 2025
% 0.13/0.34  % CPUTime    : 
% 4.22/4.39  SZS status Theorem for theBenchmark.p
% 4.22/4.39  SZS output start Proof for theBenchmark.p
% 4.22/4.39  Clause #9 (by assumption #[]): Eq
% 4.22/4.39    (∀ (W0 : Iota),
% 4.22/4.39      aSet0 W0 →
% 4.22/4.39        ∀ (W1 : Iota), Iff (aSubsetOf0 W1 W0) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 W0)))
% 4.22/4.39    True
% 4.22/4.39  Clause #13 (by assumption #[]): Eq (And (And (aSet0 xA) (aSet0 xB)) (aSet0 xC)) True
% 4.22/4.39  Clause #14 (by assumption #[]): Eq (Not (And (aSubsetOf0 xA xB) (aSubsetOf0 xB xC) → aSubsetOf0 xA xC)) True
% 4.22/4.39  Clause #35 (by clausification #[14]): Eq (And (aSubsetOf0 xA xB) (aSubsetOf0 xB xC) → aSubsetOf0 xA xC) False
% 4.22/4.39  Clause #36 (by clausification #[35]): Eq (And (aSubsetOf0 xA xB) (aSubsetOf0 xB xC)) True
% 4.22/4.39  Clause #37 (by clausification #[35]): Eq (aSubsetOf0 xA xC) False
% 4.22/4.39  Clause #38 (by clausification #[36]): Eq (aSubsetOf0 xB xC) True
% 4.22/4.39  Clause #39 (by clausification #[36]): Eq (aSubsetOf0 xA xB) True
% 4.22/4.39  Clause #57 (by clausification #[13]): Eq (aSet0 xC) True
% 4.22/4.39  Clause #58 (by clausification #[13]): Eq (And (aSet0 xA) (aSet0 xB)) True
% 4.22/4.39  Clause #65 (by clausification #[58]): Eq (aSet0 xB) True
% 4.22/4.39  Clause #66 (by clausification #[58]): Eq (aSet0 xA) True
% 4.22/4.39  Clause #72 (by clausification #[9]): ∀ (a : Iota),
% 4.22/4.39    Eq
% 4.22/4.39      (aSet0 a →
% 4.22/4.39        ∀ (W1 : Iota), Iff (aSubsetOf0 W1 a) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 a)))
% 4.22/4.39      True
% 4.22/4.39  Clause #73 (by clausification #[72]): ∀ (a : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Eq (∀ (W1 : Iota), Iff (aSubsetOf0 W1 a) (And (aSet0 W1) (∀ (W2 : Iota), aElementOf0 W2 W1 → aElementOf0 W2 a)))
% 4.22/4.39        True)
% 4.22/4.39  Clause #74 (by clausification #[73]): ∀ (a a_1 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Eq (Iff (aSubsetOf0 a_1 a) (And (aSet0 a_1) (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a))) True)
% 4.22/4.39  Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) True)
% 4.22/4.39        (Eq (And (aSet0 a_1) (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a)) False))
% 4.22/4.39  Clause #76 (by clausification #[74]): ∀ (a a_1 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) False)
% 4.22/4.39        (Eq (And (aSet0 a_1) (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a)) True))
% 4.22/4.39  Clause #77 (by clausification #[75]): ∀ (a a_1 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) True)
% 4.22/4.39        (Or (Eq (aSet0 a_1) False) (Eq (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a) False)))
% 4.22/4.39  Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) True)
% 4.22/4.39        (Or (Eq (aSet0 a_1) False)
% 4.22/4.39          (Eq (Not (aElementOf0 (skS.0 1 a_1 a a_2) a_1 → aElementOf0 (skS.0 1 a_1 a a_2) a)) True)))
% 4.22/4.39  Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) True)
% 4.22/4.39        (Or (Eq (aSet0 a_1) False) (Eq (aElementOf0 (skS.0 1 a_1 a a_2) a_1 → aElementOf0 (skS.0 1 a_1 a a_2) a) False)))
% 4.22/4.39  Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) True) (Or (Eq (aSet0 a_1) False) (Eq (aElementOf0 (skS.0 1 a_1 a a_2) a_1) True)))
% 4.22/4.39  Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) True) (Or (Eq (aSet0 a_1) False) (Eq (aElementOf0 (skS.0 1 a_1 a a_2) a) False)))
% 4.22/4.39  Clause #82 (by superposition #[80, 57]): ∀ (a a_1 : Iota),
% 4.22/4.39    Or (Eq (aSubsetOf0 a xC) True)
% 4.22/4.39      (Or (Eq (aSet0 a) False) (Or (Eq (aElementOf0 (skS.0 1 a xC a_1) a) True) (Eq False True)))
% 4.22/4.39  Clause #150 (by clausification #[76]): ∀ (a a_1 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) False) (Eq (∀ (W2 : Iota), aElementOf0 W2 a_1 → aElementOf0 W2 a) True))
% 4.22/4.39  Clause #152 (by clausification #[150]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False) (Or (Eq (aSubsetOf0 a_1 a) False) (Eq (aElementOf0 a_2 a_1 → aElementOf0 a_2 a) True))
% 4.22/4.39  Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 : Iota),
% 4.22/4.39    Or (Eq (aSet0 a) False)
% 4.22/4.39      (Or (Eq (aSubsetOf0 a_1 a) False) (Or (Eq (aElementOf0 a_2 a_1) False) (Eq (aElementOf0 a_2 a) True)))
% 4.22/4.39  Clause #154 (by superposition #[153, 57]): ∀ (a a_1 : Iota),
% 4.22/4.40    Or (Eq (aSubsetOf0 a xC) False)
% 4.22/4.40      (Or (Eq (aElementOf0 a_1 a) False) (Or (Eq (aElementOf0 a_1 xC) True) (Eq False True)))
% 4.22/4.40  Clause #155 (by superposition #[153, 65]): ∀ (a a_1 : Iota),
% 4.22/4.40    Or (Eq (aSubsetOf0 a xB) False)
% 4.22/4.40      (Or (Eq (aElementOf0 a_1 a) False) (Or (Eq (aElementOf0 a_1 xB) True) (Eq False True)))
% 4.22/4.40  Clause #166 (by superposition #[81, 57]): ∀ (a a_1 : Iota),
% 4.22/4.40    Or (Eq (aSubsetOf0 a xC) True)
% 4.22/4.40      (Or (Eq (aSet0 a) False) (Or (Eq (aElementOf0 (skS.0 1 a xC a_1) xC) False) (Eq False True)))
% 4.22/4.40  Clause #176 (by clausification #[82]): ∀ (a a_1 : Iota), Or (Eq (aSubsetOf0 a xC) True) (Or (Eq (aSet0 a) False) (Eq (aElementOf0 (skS.0 1 a xC a_1) a) True))
% 4.22/4.40  Clause #179 (by superposition #[176, 66]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xC) True) (Or (Eq (aElementOf0 (skS.0 1 xA xC a) xA) True) (Eq False True))
% 4.22/4.40  Clause #184 (by clausification #[155]): ∀ (a a_1 : Iota), Or (Eq (aSubsetOf0 a xB) False) (Or (Eq (aElementOf0 a_1 a) False) (Eq (aElementOf0 a_1 xB) True))
% 4.22/4.40  Clause #185 (by superposition #[184, 39]): ∀ (a : Iota), Or (Eq (aElementOf0 a xA) False) (Or (Eq (aElementOf0 a xB) True) (Eq False True))
% 4.22/4.40  Clause #188 (by clausification #[185]): ∀ (a : Iota), Or (Eq (aElementOf0 a xA) False) (Eq (aElementOf0 a xB) True)
% 4.22/4.40  Clause #194 (by clausification #[154]): ∀ (a a_1 : Iota), Or (Eq (aSubsetOf0 a xC) False) (Or (Eq (aElementOf0 a_1 a) False) (Eq (aElementOf0 a_1 xC) True))
% 4.22/4.40  Clause #195 (by superposition #[194, 38]): ∀ (a : Iota), Or (Eq (aElementOf0 a xB) False) (Or (Eq (aElementOf0 a xC) True) (Eq False True))
% 4.22/4.40  Clause #198 (by clausification #[195]): ∀ (a : Iota), Or (Eq (aElementOf0 a xB) False) (Eq (aElementOf0 a xC) True)
% 4.22/4.40  Clause #255 (by clausification #[166]): ∀ (a a_1 : Iota),
% 4.22/4.40    Or (Eq (aSubsetOf0 a xC) True) (Or (Eq (aSet0 a) False) (Eq (aElementOf0 (skS.0 1 a xC a_1) xC) False))
% 4.22/4.40  Clause #258 (by superposition #[255, 66]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xC) True) (Or (Eq (aElementOf0 (skS.0 1 xA xC a) xC) False) (Eq False True))
% 4.22/4.40  Clause #273 (by clausification #[179]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xC) True) (Eq (aElementOf0 (skS.0 1 xA xC a) xA) True)
% 4.22/4.40  Clause #274 (by forward demodulation #[273, 37]): ∀ (a : Iota), Or (Eq False True) (Eq (aElementOf0 (skS.0 1 xA xC a) xA) True)
% 4.22/4.40  Clause #275 (by clausification #[274]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 1 xA xC a) xA) True
% 4.22/4.40  Clause #277 (by superposition #[275, 188]): ∀ (a : Iota), Or (Eq True False) (Eq (aElementOf0 (skS.0 1 xA xC a) xB) True)
% 4.22/4.40  Clause #279 (by clausification #[277]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 1 xA xC a) xB) True
% 4.22/4.40  Clause #280 (by superposition #[279, 198]): ∀ (a : Iota), Or (Eq True False) (Eq (aElementOf0 (skS.0 1 xA xC a) xC) True)
% 4.22/4.40  Clause #281 (by clausification #[280]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 1 xA xC a) xC) True
% 4.22/4.40  Clause #341 (by clausification #[258]): ∀ (a : Iota), Or (Eq (aSubsetOf0 xA xC) True) (Eq (aElementOf0 (skS.0 1 xA xC a) xC) False)
% 4.22/4.40  Clause #342 (by forward demodulation #[341, 37]): ∀ (a : Iota), Or (Eq False True) (Eq (aElementOf0 (skS.0 1 xA xC a) xC) False)
% 4.22/4.40  Clause #343 (by clausification #[342]): ∀ (a : Iota), Eq (aElementOf0 (skS.0 1 xA xC a) xC) False
% 4.22/4.40  Clause #344 (by superposition #[343, 281]): Eq False True
% 4.22/4.40  Clause #345 (by clausification #[344]): False
% 4.22/4.40  SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------