%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : SET078-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n019.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 15:31:06 EDT 2023

% Result   : Unsatisfiable 0.21s 0.54s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET078-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % 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 : n019.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 : Sat Aug 26 14:13:58 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.21/0.54  Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.54  
% 0.21/0.54  % SZS status Unsatisfiable
% 0.21/0.54  
% 0.21/0.54  % SZS output start Proof
% 0.21/0.54  Take the following subset of the input axioms:
% 0.21/0.54    fof(prove_corollary_1_to_singletons_are_sets_1, negated_conjecture, ~member(singleton(y), unordered_pair(x, singleton(y)))).
% 0.21/0.54    fof(singleton_set, axiom, ![X]: unordered_pair(X, X)=singleton(X)).
% 0.21/0.54    fof(unordered_pair3, axiom, ![Y, X2]: (~member(Y, universal_class) | member(Y, unordered_pair(X2, Y)))).
% 0.21/0.54    fof(unordered_pairs_in_universal, axiom, ![X2, Y2]: member(unordered_pair(X2, Y2), universal_class)).
% 0.21/0.54  
% 0.21/0.54  Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.54  http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.54  We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.54    fresh(y, y, x1...xn) = u
% 0.21/0.54    C => fresh(s, t, x1...xn) = v
% 0.21/0.54  where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.54  variables of u and v.
% 0.21/0.54  A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.54  input problem has no model of domain size 1).
% 0.21/0.54  
% 0.21/0.54  The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.54  
% 0.21/0.54  Axiom 1 (singleton_set): unordered_pair(X, X) = singleton(X).
% 0.21/0.54  Axiom 2 (unordered_pairs_in_universal): member(unordered_pair(X, Y), universal_class) = true2.
% 0.21/0.54  Axiom 3 (unordered_pair3): fresh5(X, X, Y, Z) = true2.
% 0.21/0.54  Axiom 4 (unordered_pair3): fresh5(member(X, universal_class), true2, X, Y) = member(X, unordered_pair(Y, X)).
% 0.21/0.54  
% 0.21/0.54  Goal 1 (prove_corollary_1_to_singletons_are_sets_1): member(singleton(y), unordered_pair(x, singleton(y))) = true2.
% 0.21/0.54  Proof:
% 0.21/0.54    member(singleton(y), unordered_pair(x, singleton(y)))
% 0.21/0.54  = { by axiom 4 (unordered_pair3) R->L }
% 0.21/0.54    fresh5(member(singleton(y), universal_class), true2, singleton(y), x)
% 0.21/0.54  = { by axiom 1 (singleton_set) R->L }
% 0.21/0.54    fresh5(member(unordered_pair(y, y), universal_class), true2, singleton(y), x)
% 0.21/0.54  = { by axiom 2 (unordered_pairs_in_universal) }
% 0.21/0.54    fresh5(true2, true2, singleton(y), x)
% 0.21/0.54  = { by axiom 3 (unordered_pair3) }
% 0.21/0.54    true2
% 0.21/0.54  % SZS output end Proof
% 0.21/0.54  
% 0.21/0.54  RESULT: Unsatisfiable (the axioms are contradictory).
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