%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : NUM531+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 : n009.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 11:56:48 EDT 2023

% Result   : Theorem 0.18s 0.36s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : NUM531+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33  % Computer : n009.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Fri Aug 25 14:42:36 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.36  Command-line arguments: --no-flatten-goal
% 0.18/0.36  
% 0.18/0.36  % SZS status Theorem
% 0.18/0.36  
% 0.18/0.37  % SZS output start Proof
% 0.18/0.37  Take the following subset of the input axioms:
% 0.18/0.38    fof(mCountNFin, axiom, ![W0]: ((aSet0(W0) & isCountable0(W0)) => ~isFinite0(W0))).
% 0.18/0.38    fof(mDefEmp, definition, ![W0_2]: (W0_2=slcrc0 <=> (aSet0(W0_2) & ~?[W1]: aElementOf0(W1, W0_2)))).
% 0.18/0.38    fof(mEmpFin, axiom, isFinite0(slcrc0)).
% 0.18/0.38    fof(m__, conjecture, ![W0_2]: ((aSet0(W0_2) & isCountable0(W0_2)) => ~(~?[W1_2]: aElementOf0(W1_2, W0_2) & W0_2=slcrc0))).
% 0.18/0.38  
% 0.18/0.38  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.38  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.38  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.38    fresh(y, y, x1...xn) = u
% 0.18/0.38    C => fresh(s, t, x1...xn) = v
% 0.18/0.38  where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.38  variables of u and v.
% 0.18/0.38  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.38  input problem has no model of domain size 1).
% 0.18/0.38  
% 0.18/0.38  The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.38  
% 0.18/0.38  Axiom 1 (m__): w0 = slcrc0.
% 0.18/0.38  Axiom 2 (mEmpFin): isFinite0(slcrc0) = true2.
% 0.18/0.38  Axiom 3 (m___2): isCountable0(w0) = true2.
% 0.18/0.38  Axiom 4 (m___1): aSet0(w0) = true2.
% 0.18/0.38  
% 0.18/0.38  Goal 1 (mCountNFin): tuple(aSet0(X), isFinite0(X), isCountable0(X)) = tuple(true2, true2, true2).
% 0.18/0.38  The goal is true when:
% 0.18/0.38    X = slcrc0
% 0.18/0.38  
% 0.18/0.38  Proof:
% 0.18/0.38    tuple(aSet0(slcrc0), isFinite0(slcrc0), isCountable0(slcrc0))
% 0.18/0.38  = { by axiom 2 (mEmpFin) }
% 0.18/0.38    tuple(aSet0(slcrc0), true2, isCountable0(slcrc0))
% 0.18/0.38  = { by axiom 1 (m__) R->L }
% 0.18/0.38    tuple(aSet0(w0), true2, isCountable0(slcrc0))
% 0.18/0.38  = { by axiom 4 (m___1) }
% 0.18/0.38    tuple(true2, true2, isCountable0(slcrc0))
% 0.18/0.38  = { by axiom 1 (m__) R->L }
% 0.18/0.38    tuple(true2, true2, isCountable0(w0))
% 0.18/0.38  = { by axiom 3 (m___2) }
% 0.18/0.38    tuple(true2, true2, true2)
% 0.18/0.38  % SZS output end Proof
% 0.18/0.38  
% 0.18/0.38  RESULT: Theorem (the conjecture is true).
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