%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM472+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 : 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 11:56:28 EDT 2023

% Result   : Theorem 0.21s 0.53s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : NUM472+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.36  % Computer : n021.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Fri Aug 25 16:32:11 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.21/0.53  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.53  
% 0.21/0.53  % SZS status Theorem
% 0.21/0.53  
% 0.21/0.53  % SZS output start Proof
% 0.21/0.53  Take the following subset of the input axioms:
% 0.21/0.53    fof(m__, conjecture, ?[W0]: (aNaturalNumber0(W0) & sdtpldt0(xm, W0)=sdtpldt0(xm, xn)) | sdtlseqdt0(xm, sdtpldt0(xm, xn))).
% 0.21/0.53    fof(m__1324, hypothesis, aNaturalNumber0(xl) & (aNaturalNumber0(xm) & aNaturalNumber0(xn))).
% 0.21/0.53  
% 0.21/0.53  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.53  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.53  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.53    fresh(y, y, x1...xn) = u
% 0.21/0.53    C => fresh(s, t, x1...xn) = v
% 0.21/0.53  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.53  variables of u and v.
% 0.21/0.53  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.53  input problem has no model of domain size 1).
% 0.21/0.53  
% 0.21/0.53  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.53  
% 0.21/0.53  Axiom 1 (m__1324_2): aNaturalNumber0(xn) = true2.
% 0.21/0.53  
% 0.21/0.53  Goal 1 (m__): tuple(sdtpldt0(xm, X), aNaturalNumber0(X)) = tuple(sdtpldt0(xm, xn), true2).
% 0.21/0.53  The goal is true when:
% 0.21/0.53    X = xn
% 0.21/0.53  
% 0.21/0.53  Proof:
% 0.21/0.53    tuple(sdtpldt0(xm, xn), aNaturalNumber0(xn))
% 0.21/0.53  = { by axiom 1 (m__1324_2) }
% 0.21/0.53    tuple(sdtpldt0(xm, xn), true2)
% 0.21/0.53  % SZS output end Proof
% 0.21/0.53  
% 0.21/0.53  RESULT: Theorem (the conjecture is true).
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