%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET019+4 : TPTP v8.1.2. Released v2.2.0.
% 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 : n025.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 15:30:38 EDT 2023

% Result   : Theorem 0.19s 0.41s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET019+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 16:22:08 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.41  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.41  
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  
% 0.19/0.42  % SZS output start Proof
% 0.19/0.42  Take the following subset of the input axioms:
% 0.19/0.42    fof(equal_set, axiom, ![B, A2]: (equal_set(A2, B) <=> (subset(A2, B) & subset(B, A2)))).
% 0.19/0.42    fof(thI02, conjecture, ![A, B2]: ((subset(A, B2) & subset(B2, A)) => equal_set(A, B2))).
% 0.19/0.42  
% 0.19/0.42  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.42  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.42  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.42    fresh(y, y, x1...xn) = u
% 0.19/0.42    C => fresh(s, t, x1...xn) = v
% 0.19/0.42  where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.42  variables of u and v.
% 0.19/0.42  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.42  input problem has no model of domain size 1).
% 0.19/0.42  
% 0.19/0.42  The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.42  
% 0.19/0.42  Axiom 1 (thI02): subset(a, b) = true2.
% 0.19/0.42  Axiom 2 (thI02_1): subset(b, a) = true2.
% 0.19/0.42  Axiom 3 (equal_set): fresh24(X, X, Y, Z) = equal_set(Y, Z).
% 0.19/0.42  Axiom 4 (equal_set): fresh22(X, X, Y, Z) = true2.
% 0.19/0.42  Axiom 5 (equal_set): fresh24(subset(X, Y), true2, Y, X) = fresh22(subset(Y, X), true2, Y, X).
% 0.19/0.42  
% 0.19/0.42  Goal 1 (thI02_2): equal_set(a, b) = true2.
% 0.19/0.42  Proof:
% 0.19/0.42    equal_set(a, b)
% 0.19/0.42  = { by axiom 3 (equal_set) R->L }
% 0.19/0.42    fresh24(true2, true2, a, b)
% 0.19/0.42  = { by axiom 2 (thI02_1) R->L }
% 0.19/0.42    fresh24(subset(b, a), true2, a, b)
% 0.19/0.42  = { by axiom 5 (equal_set) }
% 0.19/0.42    fresh22(subset(a, b), true2, a, b)
% 0.19/0.42  = { by axiom 1 (thI02) }
% 0.19/0.42    fresh22(true2, true2, a, b)
% 0.19/0.42  = { by axiom 4 (equal_set) }
% 0.19/0.42    true2
% 0.19/0.42  % SZS output end Proof
% 0.19/0.42  
% 0.19/0.42  RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------