%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PUZ063-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% 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  : 600s
% DateTime : Mon Jul 18 18:20:56 EDT 2022

% Result   : Unsatisfiable 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :   11 (   3 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :    2 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
    c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ).

cnf(cls_conjecture_2,negated_conjecture,
    ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ).

cnf(cls_Set_OUn__empty__left_0,axiom,
    c_union(c_emptyset,V_y,T_a) = V_y ).

cnf(refute_0_0,plain,
    c_union(c_emptyset,v_u,t_a) = v_u,
    inference(subst,[],[cls_Set_OUn__empty__left_0:[bind(T_a,$fot(t_a)),bind(V_y,$fot(v_u))]]) ).

cnf(refute_0_1,plain,
    ( c_union(c_emptyset,v_u,t_a) != v_u
    | ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
    | c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
    introduced(tautology,[equality,[$cnf( ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),[0],$fot(v_u)]]) ).

cnf(refute_0_2,plain,
    ( ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
    | c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ),
    inference(resolve,[$cnf( $equal(c_union(c_emptyset,v_u,t_a),v_u) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)),
    inference(resolve,[$cnf( c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) )],[refute_0_2,cls_conjecture_2]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) )],[cls_conjecture_0,refute_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ063-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n019.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 : Sat May 28 20:57:26 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------