%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 20:29:47 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   4 nHn;  10 RR)
%            Number of literals    :   18 (   0 equ;   6 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :    2 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause_1,negated_conjecture,
    ~ less_than(n,k) ).

cnf(clause_2,negated_conjecture,
    ~ less_than(k,l) ).

cnf(clause_5,negated_conjecture,
    less_than(one,l) ).

cnf(clause_6,negated_conjecture,
    less_than(a(k),a(predecessor(l))) ).

cnf(clause_8,negated_conjecture,
    ( less_than(X,l)
    | less_than(n,X)
    | ~ less_than(one,l)
    | ~ less_than(a(X),a(predecessor(l))) ) ).

cnf(refute_0_0,plain,
    ( ~ less_than(a(X),a(predecessor(l)))
    | less_than(X,l)
    | less_than(n,X) ),
    inference(resolve,[$cnf( less_than(one,l) )],[clause_5,clause_8]) ).

cnf(refute_0_1,plain,
    ( ~ less_than(a(k),a(predecessor(l)))
    | less_than(k,l)
    | less_than(n,k) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(k))]]) ).

cnf(refute_0_2,plain,
    ( less_than(k,l)
    | less_than(n,k) ),
    inference(resolve,[$cnf( less_than(a(k),a(predecessor(l))) )],[clause_6,refute_0_1]) ).

cnf(refute_0_3,plain,
    less_than(n,k),
    inference(resolve,[$cnf( less_than(k,l) )],[refute_0_2,clause_2]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( less_than(n,k) )],[refute_0_3,clause_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n029.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 : Thu Jun 16 06:22:42 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------