%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM550+3 : 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 : n021.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 11:56:55 EDT 2023

% Result   : Theorem 2.04s 0.74s
% Output   : Proof 2.04s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM550+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.37  % Computer : n021.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Fri Aug 25 13:13:40 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 2.04/0.74  Command-line arguments: --ground-connectedness --complete-subsets
% 2.04/0.74  
% 2.04/0.74  % SZS status Theorem
% 2.04/0.74  
% 2.04/0.74  % SZS output start Proof
% 2.04/0.74  Take the following subset of the input axioms:
% 2.04/0.74    fof(mCardEmpty, axiom, ![W0]: (aSet0(W0) => (sbrdtbr0(W0)=sz00 <=> W0=slcrc0))).
% 2.04/0.74    fof(m__, conjecture, ~(~?[W0_2]: aElementOf0(W0_2, xQ) & xQ=slcrc0)).
% 2.04/0.74    fof(m__2202_02, hypothesis, aSet0(xS) & (aSet0(xT) & xk!=sz00)).
% 2.04/0.74    fof(m__2270, hypothesis, aSet0(xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => aElementOf0(W0_2, xS)) & (aSubsetOf0(xQ, xS) & (sbrdtbr0(xQ)=xk & aElementOf0(xQ, slbdtsldtrb0(xS, xk)))))).
% 2.04/0.74  
% 2.04/0.74  Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.04/0.74  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.04/0.74  We repeatedly replace C & s=t => u=v by the two clauses:
% 2.04/0.74    fresh(y, y, x1...xn) = u
% 2.04/0.74    C => fresh(s, t, x1...xn) = v
% 2.04/0.74  where fresh is a fresh function symbol and x1..xn are the free
% 2.04/0.74  variables of u and v.
% 2.04/0.74  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.04/0.74  input problem has no model of domain size 1).
% 2.04/0.74  
% 2.04/0.74  The encoding turns the above axioms into the following unit equations and goals:
% 2.04/0.74  
% 2.04/0.74  Axiom 1 (m__): xQ = slcrc0.
% 2.04/0.74  Axiom 2 (m__2270): sbrdtbr0(xQ) = xk.
% 2.04/0.74  Axiom 3 (m__2270_1): aSet0(xQ) = true2.
% 2.04/0.74  Axiom 4 (mCardEmpty): fresh92(X, X, Y) = sz00.
% 2.04/0.74  Axiom 5 (mCardEmpty): fresh91(X, X, Y) = sbrdtbr0(Y).
% 2.04/0.74  Axiom 6 (mCardEmpty): fresh91(aSet0(X), true2, X) = fresh92(X, slcrc0, X).
% 2.04/0.74  
% 2.04/0.74  Goal 1 (m__2202_02_2): xk = sz00.
% 2.04/0.74  Proof:
% 2.04/0.74    xk
% 2.04/0.74  = { by axiom 2 (m__2270) R->L }
% 2.04/0.74    sbrdtbr0(xQ)
% 2.04/0.74  = { by axiom 5 (mCardEmpty) R->L }
% 2.04/0.74    fresh91(true2, true2, xQ)
% 2.04/0.74  = { by axiom 3 (m__2270_1) R->L }
% 2.04/0.74    fresh91(aSet0(xQ), true2, xQ)
% 2.04/0.74  = { by axiom 6 (mCardEmpty) }
% 2.04/0.74    fresh92(xQ, slcrc0, xQ)
% 2.04/0.74  = { by axiom 1 (m__) R->L }
% 2.04/0.74    fresh92(xQ, xQ, xQ)
% 2.04/0.74  = { by axiom 4 (mCardEmpty) }
% 2.04/0.74    sz00
% 2.04/0.74  % SZS output end Proof
% 2.04/0.74  
% 2.04/0.74  RESULT: Theorem (the conjecture is true).
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