%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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  : 600s
% DateTime : Tue Jul 19 03:31:27 EDT 2022

% Result   : Unsatisfiable 271.21s 271.44s
% Output   : CNFRefutation 271.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   16 (   9 unt;   0 nHn;  14 RR)
%            Number of literals    :   25 (  13 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :    8 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(ordered_pair_predicate3,axiom,
    ( ~ ordered_pair_predicate(X)
    | X = ordered_pair(f2(X),f3(X)) ) ).

cnf(ordered_pairs_are_small1,axiom,
    little_set(ordered_pair(X,Y)) ).

cnf(an_ordered_pair_predicate,hypothesis,
    ordered_pair_predicate(a) ).

cnf(prove_predicate_is_small,negated_conjecture,
    ~ little_set(a) ).

cnf(refute_0_0,plain,
    little_set(ordered_pair(f2(a),f3(a))),
    inference(subst,[],[ordered_pairs_are_small1:[bind(X,$fot(f2(a))),bind(Y,$fot(f3(a)))]]) ).

cnf(refute_0_1,plain,
    ( ~ ordered_pair_predicate(a)
    | a = ordered_pair(f2(a),f3(a)) ),
    inference(subst,[],[ordered_pair_predicate3:[bind(X,$fot(a))]]) ).

cnf(refute_0_2,plain,
    a = ordered_pair(f2(a),f3(a)),
    inference(resolve,[$cnf( ordered_pair_predicate(a) )],[an_ordered_pair_predicate,refute_0_1]) ).

cnf(refute_0_3,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_5,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( a != ordered_pair(f2(a),f3(a))
    | ordered_pair(f2(a),f3(a)) = a ),
    inference(subst,[],[refute_0_5:[bind(X0,$fot(a)),bind(Y0,$fot(ordered_pair(f2(a),f3(a))))]]) ).

cnf(refute_0_7,plain,
    ordered_pair(f2(a),f3(a)) = a,
    inference(resolve,[$cnf( $equal(a,ordered_pair(f2(a),f3(a))) )],[refute_0_2,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ordered_pair(f2(a),f3(a)) != a
    | ~ little_set(ordered_pair(f2(a),f3(a)))
    | little_set(a) ),
    introduced(tautology,[equality,[$cnf( little_set(ordered_pair(f2(a),f3(a))) ),[0],$fot(a)]]) ).

cnf(refute_0_9,plain,
    ( ~ little_set(ordered_pair(f2(a),f3(a)))
    | little_set(a) ),
    inference(resolve,[$cnf( $equal(ordered_pair(f2(a),f3(a)),a) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    little_set(a),
    inference(resolve,[$cnf( little_set(ordered_pair(f2(a),f3(a))) )],[refute_0_0,refute_0_9]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( little_set(a) )],[refute_0_10,prove_predicate_is_small]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET025-8 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n008.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  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 05:52:08 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 271.21/271.44  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 271.21/271.44  
% 271.21/271.44  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 271.21/271.44  
%------------------------------------------------------------------------------