%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET117+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n007.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 15:31:21 EDT 2023

% Result   : Theorem 0.18s 0.50s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET117+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 10:40:11 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.50  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.18/0.50  
% 0.18/0.50  % SZS status Theorem
% 0.18/0.50  
% 0.18/0.50  % SZS output start Proof
% 0.18/0.50  Take the following subset of the input axioms:
% 0.18/0.50    fof(corollary_1_to_ordered_pairs_are_sets, conjecture, ![X]: (ordered_pair(first(X), second(X))=X => member(X, universal_class))).
% 0.18/0.50    fof(ordered_pair_defn, axiom, ![Y, X2]: ordered_pair(X2, Y)=unordered_pair(singleton(X2), unordered_pair(X2, singleton(Y)))).
% 0.18/0.50    fof(unordered_pair, axiom, ![X2, Y2]: member(unordered_pair(X2, Y2), universal_class)).
% 0.18/0.50  
% 0.18/0.50  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.50  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.50  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.50    fresh(y, y, x1...xn) = u
% 0.18/0.50    C => fresh(s, t, x1...xn) = v
% 0.18/0.50  where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.50  variables of u and v.
% 0.18/0.50  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.50  input problem has no model of domain size 1).
% 0.18/0.50  
% 0.18/0.50  The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.50  
% 0.18/0.50  Axiom 1 (unordered_pair): member(unordered_pair(X, Y), universal_class) = true2.
% 0.18/0.50  Axiom 2 (corollary_1_to_ordered_pairs_are_sets): ordered_pair(first(x), second(x)) = x.
% 0.18/0.50  Axiom 3 (ordered_pair_defn): ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))).
% 0.18/0.50  
% 0.18/0.50  Goal 1 (corollary_1_to_ordered_pairs_are_sets_1): member(x, universal_class) = true2.
% 0.18/0.50  Proof:
% 0.18/0.50    member(x, universal_class)
% 0.18/0.50  = { by axiom 2 (corollary_1_to_ordered_pairs_are_sets) R->L }
% 0.18/0.50    member(ordered_pair(first(x), second(x)), universal_class)
% 0.18/0.50  = { by axiom 3 (ordered_pair_defn) }
% 0.18/0.50    member(unordered_pair(singleton(first(x)), unordered_pair(first(x), singleton(second(x)))), universal_class)
% 0.18/0.50  = { by axiom 1 (unordered_pair) }
% 0.18/0.50    true2
% 0.18/0.50  % SZS output end Proof
% 0.18/0.50  
% 0.18/0.50  RESULT: Theorem (the conjecture is true).
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