%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SEU085+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n017.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 17:50:58 EDT 2023

% Result   : Theorem 0.21s 0.51s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU085+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % 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 : n017.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 : Wed Aug 23 19:53:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.51  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.51  
% 0.21/0.51  % SZS status Theorem
% 0.21/0.51  
% 0.21/0.51  % SZS output start Proof
% 0.21/0.51  Take the following subset of the input axioms:
% 0.21/0.51    fof(fc12_finset_1, axiom, ![B, A2]: (finite(A2) => finite(set_difference(A2, B)))).
% 0.21/0.51    fof(t16_finset_1, conjecture, ![A, B2]: (finite(A) => finite(set_difference(A, B2)))).
% 0.21/0.51  
% 0.21/0.51  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.51  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.51  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.51    fresh(y, y, x1...xn) = u
% 0.21/0.51    C => fresh(s, t, x1...xn) = v
% 0.21/0.51  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.51  variables of u and v.
% 0.21/0.51  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.51  input problem has no model of domain size 1).
% 0.21/0.51  
% 0.21/0.51  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.51  
% 0.21/0.51  Axiom 1 (t16_finset_1): finite(a) = true2.
% 0.21/0.51  Axiom 2 (fc12_finset_1): fresh15(X, X, Y, Z) = true2.
% 0.21/0.51  Axiom 3 (fc12_finset_1): fresh15(finite(X), true2, X, Y) = finite(set_difference(X, Y)).
% 0.21/0.51  
% 0.21/0.51  Goal 1 (t16_finset_1_1): finite(set_difference(a, b)) = true2.
% 0.21/0.51  Proof:
% 0.21/0.51    finite(set_difference(a, b))
% 0.21/0.51  = { by axiom 3 (fc12_finset_1) R->L }
% 0.21/0.51    fresh15(finite(a), true2, a, b)
% 0.21/0.51  = { by axiom 1 (t16_finset_1) }
% 0.21/0.51    fresh15(true2, true2, a, b)
% 0.21/0.51  = { by axiom 2 (fc12_finset_1) }
% 0.21/0.51    true2
% 0.21/0.51  % SZS output end Proof
% 0.21/0.51  
% 0.21/0.51  RESULT: Theorem (the conjecture is true).
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