%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM533+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n029.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 11:56:49 EDT 2023

% Result   : Theorem 0.13s 0.41s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM533+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 : Fri Aug 25 11:33:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.41  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.13/0.41  
% 0.13/0.41  % SZS status Theorem
% 0.13/0.41  
% 0.13/0.41  % SZS output start Proof
% 0.13/0.41  Take the following subset of the input axioms:
% 0.13/0.41    fof(m__, conjecture, (![W0]: (aElementOf0(W0, xA) => aElementOf0(W0, xB)) & (aSubsetOf0(xA, xB) & (![W0_2]: (aElementOf0(W0_2, xB) => aElementOf0(W0_2, xC)) & aSubsetOf0(xB, xC)))) => (![W0_2]: (aElementOf0(W0_2, xA) => aElementOf0(W0_2, xC)) | aSubsetOf0(xA, xC))).
% 0.13/0.41  
% 0.13/0.41  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.41  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.41  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.41    fresh(y, y, x1...xn) = u
% 0.13/0.41    C => fresh(s, t, x1...xn) = v
% 0.13/0.41  where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.41  variables of u and v.
% 0.13/0.41  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.41  input problem has no model of domain size 1).
% 0.13/0.41  
% 0.13/0.41  The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.41  
% 0.13/0.41  Axiom 1 (m__): aElementOf0(w0, xA) = true2.
% 0.13/0.41  Axiom 2 (m___4): fresh(X, X, Y) = true2.
% 0.13/0.41  Axiom 3 (m___3): fresh2(X, X, Y) = true2.
% 0.13/0.41  Axiom 4 (m___4): fresh(aElementOf0(X, xB), true2, X) = aElementOf0(X, xC).
% 0.13/0.41  Axiom 5 (m___3): fresh2(aElementOf0(X, xA), true2, X) = aElementOf0(X, xB).
% 0.13/0.41  
% 0.13/0.41  Goal 1 (m___5): aElementOf0(w0, xC) = true2.
% 0.13/0.41  Proof:
% 0.13/0.41    aElementOf0(w0, xC)
% 0.13/0.41  = { by axiom 4 (m___4) R->L }
% 0.13/0.41    fresh(aElementOf0(w0, xB), true2, w0)
% 0.13/0.41  = { by axiom 5 (m___3) R->L }
% 0.13/0.41    fresh(fresh2(aElementOf0(w0, xA), true2, w0), true2, w0)
% 0.13/0.41  = { by axiom 1 (m__) }
% 0.13/0.41    fresh(fresh2(true2, true2, w0), true2, w0)
% 0.13/0.41  = { by axiom 3 (m___3) }
% 0.13/0.41    fresh(true2, true2, w0)
% 0.13/0.41  = { by axiom 2 (m___4) }
% 0.13/0.41    true2
% 0.13/0.41  % SZS output end Proof
% 0.13/0.41  
% 0.13/0.41  RESULT: Theorem (the conjecture is true).
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