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% File     : Twee---2.4.2
% Problem  : NUM458+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 : n006.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 11:56:24 EDT 2023

% Result   : Theorem 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM458+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n006.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 09:14:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.44  Command-line arguments: --ground-connectedness --complete-subsets
% 0.20/0.44  
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  
% 0.20/0.44  % SZS output start Proof
% 0.20/0.44  Take the following subset of the input axioms:
% 0.20/0.44    fof(mSortsC, axiom, aNaturalNumber0(sz00)).
% 0.20/0.44    fof(m_AddZero, axiom, ![W0]: (aNaturalNumber0(W0) => (sdtpldt0(W0, sz00)=W0 & W0=sdtpldt0(sz00, W0)))).
% 0.20/0.44    fof(m__, conjecture, ?[W0_2]: (aNaturalNumber0(W0_2) & sdtpldt0(xm, W0_2)=xm) | sdtlseqdt0(xm, xm)).
% 0.20/0.44    fof(m__718, hypothesis, aNaturalNumber0(xm)).
% 0.20/0.44  
% 0.20/0.44  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.44  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.44  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.44    fresh(y, y, x1...xn) = u
% 0.20/0.44    C => fresh(s, t, x1...xn) = v
% 0.20/0.44  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.44  variables of u and v.
% 0.20/0.44  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.44  input problem has no model of domain size 1).
% 0.20/0.44  
% 0.20/0.44  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.44  
% 0.20/0.44  Axiom 1 (m__718): aNaturalNumber0(xm) = true2.
% 0.20/0.44  Axiom 2 (mSortsC): aNaturalNumber0(sz00) = true2.
% 0.20/0.44  Axiom 3 (m_AddZero): fresh9(X, X, Y) = Y.
% 0.20/0.44  Axiom 4 (m_AddZero): fresh9(aNaturalNumber0(X), true2, X) = sdtpldt0(X, sz00).
% 0.20/0.44  
% 0.20/0.44  Goal 1 (m__): tuple(sdtpldt0(xm, X), aNaturalNumber0(X)) = tuple(xm, true2).
% 0.20/0.44  The goal is true when:
% 0.20/0.44    X = sz00
% 0.20/0.44  
% 0.20/0.44  Proof:
% 0.20/0.44    tuple(sdtpldt0(xm, sz00), aNaturalNumber0(sz00))
% 0.20/0.44  = { by axiom 4 (m_AddZero) R->L }
% 0.20/0.44    tuple(fresh9(aNaturalNumber0(xm), true2, xm), aNaturalNumber0(sz00))
% 0.20/0.44  = { by axiom 1 (m__718) }
% 0.20/0.44    tuple(fresh9(true2, true2, xm), aNaturalNumber0(sz00))
% 0.20/0.44  = { by axiom 3 (m_AddZero) }
% 0.20/0.44    tuple(xm, aNaturalNumber0(sz00))
% 0.20/0.44  = { by axiom 2 (mSortsC) }
% 0.20/0.44    tuple(xm, true2)
% 0.20/0.44  % SZS output end Proof
% 0.20/0.44  
% 0.20/0.44  RESULT: Theorem (the conjecture is true).
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