%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM430+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 : n002.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 11:56:14 EDT 2023

% Result   : Theorem 0.20s 0.46s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM430+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri Aug 25 10:51:47 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.46  Command-line arguments: --no-flatten-goal
% 0.20/0.46  
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  
% 0.20/0.46  % SZS output start Proof
% 0.20/0.46  Take the following subset of the input axioms:
% 0.20/0.46    fof(mDivisor, definition, ![W0]: (aInteger0(W0) => ![W1]: (aDivisorOf0(W1, W0) <=> (aInteger0(W1) & (W1!=sz00 & ?[W2]: (aInteger0(W2) & sdtasdt0(W1, W2)=W0)))))).
% 0.20/0.46    fof(m__, conjecture, ?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xq, W0_2)=sdtpldt0(xb, smndt0(xc)))).
% 0.20/0.46    fof(m__853, hypothesis, ?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xq, W0_2)=sdtpldt0(xa, smndt0(xb))) & (aDivisorOf0(xq, sdtpldt0(xa, smndt0(xb))) & (sdteqdtlpzmzozddtrp0(xa, xb, xq) & (?[W0_2]: (aInteger0(W0_2) & sdtasdt0(xq, W0_2)=sdtpldt0(xb, smndt0(xc))) & (aDivisorOf0(xq, sdtpldt0(xb, smndt0(xc))) & sdteqdtlpzmzozddtrp0(xb, xc, xq)))))).
% 0.20/0.46  
% 0.20/0.46  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.46  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.46  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.46    fresh(y, y, x1...xn) = u
% 0.20/0.46    C => fresh(s, t, x1...xn) = v
% 0.20/0.46  where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.46  variables of u and v.
% 0.20/0.46  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.46  input problem has no model of domain size 1).
% 0.20/0.46  
% 0.20/0.46  The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.46  
% 0.20/0.46  Axiom 1 (m__853_3): aInteger0(w0) = true2.
% 0.20/0.46  Axiom 2 (m__853_1): sdtasdt0(xq, w0) = sdtpldt0(xb, smndt0(xc)).
% 0.20/0.46  
% 0.20/0.46  Goal 1 (m__): tuple2(sdtasdt0(xq, X), aInteger0(X)) = tuple2(sdtpldt0(xb, smndt0(xc)), true2).
% 0.20/0.46  The goal is true when:
% 0.20/0.46    X = w0
% 0.20/0.46  
% 0.20/0.46  Proof:
% 0.20/0.46    tuple2(sdtasdt0(xq, w0), aInteger0(w0))
% 0.20/0.46  = { by axiom 1 (m__853_3) }
% 0.20/0.46    tuple2(sdtasdt0(xq, w0), true2)
% 0.20/0.46  = { by axiom 2 (m__853_1) }
% 0.20/0.46    tuple2(sdtpldt0(xb, smndt0(xc)), true2)
% 0.20/0.46  % SZS output end Proof
% 0.20/0.46  
% 0.20/0.46  RESULT: Theorem (the conjecture is true).
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