## TPTP Problem File: SET047-5.p

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```%--------------------------------------------------------------------------
% File     : SET047-5 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Set Theory
% Problem  : Set equality is symmetric
% Version  : [Pel86] axioms : Incomplete.
% English  : Define set equality as having exactly the same members. Prove
%            set equality is symmetric.

% Refs     : [DeC79] DeChampeaux (1979), Sub-problem Finder and Instance Ch
%          : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% Source   : [Pel86]
% Names    : Pelletier 43 [Pel86]
%          : p43.in [ANL]

% Status   : Unsatisfiable
% Rating   : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v5.1.0, 0.09 v5.0.0, 0.07 v4.1.0, 0.12 v4.0.1, 0.00 v2.1.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :    6 (   0 unt;   2 nHn;   5 RR)
%            Number of literals    :   16 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   10 (   0 sgn)
% SPC      : CNF_UNS_RFO_NEQ_NHN

%--------------------------------------------------------------------------
cnf(element_substitution1,axiom,
( ~ set_equal(X,Y)
| ~ element(Z,X)
| element(Z,Y) ) ).

cnf(element_substitution2,axiom,
( ~ set_equal(X,Y)
| ~ element(Z,Y)
| element(Z,X) ) ).

cnf(clause_3,axiom,
( element(f(X,Y),X)
| element(f(X,Y),Y)
| set_equal(X,Y) ) ).

cnf(clause_4,axiom,
( ~ element(f(X,Y),Y)
| ~ element(f(X,Y),X)
| set_equal(X,Y) ) ).

cnf(prove_symmetry1,negated_conjecture,
( set_equal(a,b)
| set_equal(b,a) ) ).

cnf(prove_symmetry2,negated_conjecture,
( ~ set_equal(b,a)
| ~ set_equal(a,b) ) ).

%--------------------------------------------------------------------------
```