%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   5 unt;   0 nHn;   9 RR)
%            Number of literals    :   15 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    5 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(transitivity_of_less_than,axiom,
    ( less_than(X,Z)
    | ~ less_than(X,Y)
    | ~ less_than(Y,Z) ) ).

cnf(clause_2,negated_conjecture,
    less_than(k,j) ).

cnf(clause_3,negated_conjecture,
    ~ less_than(k,i) ).

cnf(clause_9,negated_conjecture,
    less_than(j,i) ).

cnf(refute_0_0,plain,
    ( ~ less_than(j,X_20)
    | ~ less_than(k,j)
    | less_than(k,X_20) ),
    inference(subst,[],[transitivity_of_less_than:[bind(X,$fot(k)),bind(Y,$fot(j)),bind(Z,$fot(X_20))]]) ).

cnf(refute_0_1,plain,
    ( ~ less_than(j,X_20)
    | less_than(k,X_20) ),
    inference(resolve,[$cnf( less_than(k,j) )],[clause_2,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ less_than(j,i)
    | less_than(k,i) ),
    inference(subst,[],[refute_0_1:[bind(X_20,$fot(i))]]) ).

cnf(refute_0_3,plain,
    less_than(k,i),
    inference(resolve,[$cnf( less_than(j,i) )],[clause_9,refute_0_2]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( less_than(k,i) )],[refute_0_3,clause_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun 15 14:12:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------