%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 : Wed Jul 20 20:30:41 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   20 (  13 unt;   0 nHn;  13 RR)
%            Number of literals    :   31 (  17 equ;  13 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   16 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | ~ c_lessequals(V_n,V_m,T_a)
    | c_SetInterval_OatLeastLessThan(V_m,V_n,T_a) = c_emptyset ) ).

cnf(cls_SetInterval_OatLeastLessThan__singleton_0,axiom,
    c_SetInterval_OatLeastLessThan(V_m,c_Suc(V_m),tc_nat) = c_insert(V_m,c_emptyset,tc_nat) ).

cnf(cls_Set_Oempty__not__insert_0,axiom,
    c_emptyset != c_insert(V_a,V_A,T_a) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_lessequals(V_U,v_x(V_U),tc_nat) ).

cnf(cls_conjecture_1,negated_conjecture,
    v_x(V_U) = v_nat ).

cnf(clsarity_nat_3,axiom,
    class_Orderings_Oorder(tc_nat) ).

cnf(refute_0_0,plain,
    c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_insert(v_nat,c_emptyset,tc_nat),
    inference(subst,[],[cls_SetInterval_OatLeastLessThan__singleton_0:[bind(V_m,$fot(v_nat))]]) ).

cnf(refute_0_1,plain,
    ( v_x(V_U) != v_nat
    | ~ c_lessequals(V_U,v_x(V_U),tc_nat)
    | c_lessequals(V_U,v_nat,tc_nat) ),
    introduced(tautology,[equality,[$cnf( c_lessequals(V_U,v_x(V_U),tc_nat) ),[1],$fot(v_nat)]]) ).

cnf(refute_0_2,plain,
    ( ~ c_lessequals(V_U,v_x(V_U),tc_nat)
    | c_lessequals(V_U,v_nat,tc_nat) ),
    inference(resolve,[$cnf( $equal(v_x(V_U),v_nat) )],[cls_conjecture_1,refute_0_1]) ).

cnf(refute_0_3,plain,
    c_lessequals(V_U,v_nat,tc_nat),
    inference(resolve,[$cnf( c_lessequals(V_U,v_x(V_U),tc_nat) )],[cls_conjecture_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    c_lessequals(X_8,v_nat,tc_nat),
    inference(subst,[],[refute_0_3:[bind(V_U,$fot(X_8))]]) ).

cnf(refute_0_5,plain,
    ( ~ c_lessequals(X_8,v_nat,tc_nat)
    | ~ class_Orderings_Oorder(tc_nat)
    | c_SetInterval_OatLeastLessThan(v_nat,X_8,tc_nat) = c_emptyset ),
    inference(subst,[],[cls_SetInterval_OatLeastLessThan__empty_0:[bind(T_a,$fot(tc_nat)),bind(V_m,$fot(v_nat)),bind(V_n,$fot(X_8))]]) ).

cnf(refute_0_6,plain,
    ( ~ class_Orderings_Oorder(tc_nat)
    | c_SetInterval_OatLeastLessThan(v_nat,X_8,tc_nat) = c_emptyset ),
    inference(resolve,[$cnf( c_lessequals(X_8,v_nat,tc_nat) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    c_SetInterval_OatLeastLessThan(v_nat,X_8,tc_nat) = c_emptyset,
    inference(resolve,[$cnf( class_Orderings_Oorder(tc_nat) )],[clsarity_nat_3,refute_0_6]) ).

cnf(refute_0_8,plain,
    c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) = c_emptyset,
    inference(subst,[],[refute_0_7:[bind(X_8,$fot(c_Suc(v_nat)))]]) ).

cnf(refute_0_9,plain,
    ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) != c_emptyset
    | c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) != c_insert(v_nat,c_emptyset,tc_nat)
    | c_emptyset = c_insert(v_nat,c_emptyset,tc_nat) ),
    introduced(tautology,[equality,[$cnf( $equal(c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat),c_insert(v_nat,c_emptyset,tc_nat)) ),[0],$fot(c_emptyset)]]) ).

cnf(refute_0_10,plain,
    ( c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat) != c_insert(v_nat,c_emptyset,tc_nat)
    | c_emptyset = c_insert(v_nat,c_emptyset,tc_nat) ),
    inference(resolve,[$cnf( $equal(c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat),c_emptyset) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    c_emptyset = c_insert(v_nat,c_emptyset,tc_nat),
    inference(resolve,[$cnf( $equal(c_SetInterval_OatLeastLessThan(v_nat,c_Suc(v_nat),tc_nat),c_insert(v_nat,c_emptyset,tc_nat)) )],[refute_0_0,refute_0_10]) ).

cnf(refute_0_12,plain,
    c_emptyset != c_insert(v_nat,c_emptyset,tc_nat),
    inference(subst,[],[cls_Set_Oempty__not__insert_0:[bind(T_a,$fot(tc_nat)),bind(V_A,$fot(c_emptyset)),bind(V_a,$fot(v_nat))]]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( $equal(c_emptyset,c_insert(v_nat,c_emptyset,tc_nat)) )],[refute_0_11,refute_0_12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Wed Jun 15 19:46:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------