%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SEU382+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n032.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 17:52:29 EDT 2023

% Result   : Theorem 249.47s 32.43s
% Output   : Proof 249.47s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEU382+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Wed Aug 23 22:39:26 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 249.47/32.43  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 249.47/32.43  
% 249.47/32.43  % SZS status Theorem
% 249.47/32.43  
% 249.47/32.43  % SZS output start Proof
% 249.47/32.43  Take the following subset of the input axioms:
% 249.47/32.43    fof(t1_yellow_1, lemma, ![A]: (the_carrier(incl_POSet(A))=A & the_InternalRel(incl_POSet(A))=inclusion_order(A))).
% 249.47/32.43    fof(t4_waybel_7, conjecture, ![A2]: the_carrier(boole_POSet(A2))=powerset(A2)).
% 249.47/32.43    fof(t4_yellow_1, lemma, ![A2]: boole_POSet(A2)=incl_POSet(powerset(A2))).
% 249.47/32.43  
% 249.47/32.43  Now clausify the problem and encode Horn clauses using encoding 3 of
% 249.47/32.43  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 249.47/32.43  We repeatedly replace C & s=t => u=v by the two clauses:
% 249.47/32.43    fresh(y, y, x1...xn) = u
% 249.47/32.43    C => fresh(s, t, x1...xn) = v
% 249.47/32.43  where fresh is a fresh function symbol and x1..xn are the free
% 249.47/32.43  variables of u and v.
% 249.47/32.43  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 249.47/32.43  input problem has no model of domain size 1).
% 249.47/32.43  
% 249.47/32.43  The encoding turns the above axioms into the following unit equations and goals:
% 249.47/32.43  
% 249.47/32.43  Axiom 1 (t1_yellow_1): the_carrier(incl_POSet(X)) = X.
% 249.47/32.43  Axiom 2 (t4_yellow_1): boole_POSet(X) = incl_POSet(powerset(X)).
% 249.47/32.43  
% 249.47/32.43  Goal 1 (t4_waybel_7): the_carrier(boole_POSet(a)) = powerset(a).
% 249.47/32.43  Proof:
% 249.47/32.43    the_carrier(boole_POSet(a))
% 249.47/32.43  = { by axiom 2 (t4_yellow_1) }
% 249.47/32.43    the_carrier(incl_POSet(powerset(a)))
% 249.47/32.43  = { by axiom 1 (t1_yellow_1) }
% 249.47/32.43    powerset(a)
% 249.47/32.43  % SZS output end Proof
% 249.47/32.43  
% 249.47/32.43  RESULT: Theorem (the conjecture is true).
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