%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL169-3 : TPTP v8.1.0. Released v2.3.0.
% 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 : Sun Jul 17 12:50:09 EDT 2022

% Result   : Unsatisfiable 0.14s 0.35s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   18 (  11 unt;   0 nHn;  10 RR)
%            Number of literals    :   27 (  12 equ;  10 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   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   :   18 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
    axiom(implies(or(A,A),A)) ).

cnf(implies_definition,axiom,
    implies(X,Y) = or(not(X),Y) ).

cnf(rule_1,axiom,
    ( theorem(X)
    | ~ axiom(X) ) ).

cnf(prove_this,negated_conjecture,
    ~ theorem(implies(implies(p,not(p)),not(p))) ).

cnf(refute_0_0,plain,
    ( ~ axiom(implies(or(A,A),A))
    | theorem(implies(or(A,A),A)) ),
    inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).

cnf(refute_0_1,plain,
    theorem(implies(or(A,A),A)),
    inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_0]) ).

cnf(refute_0_2,plain,
    theorem(implies(or(not(X_5),not(X_5)),not(X_5))),
    inference(subst,[],[refute_0_1:[bind(A,$fot(not(X_5)))]]) ).

cnf(refute_0_3,plain,
    implies(X_5,not(X_5)) = or(not(X_5),not(X_5)),
    inference(subst,[],[implies_definition:[bind(X,$fot(X_5)),bind(Y,$fot(not(X_5)))]]) ).

cnf(refute_0_4,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_5,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( implies(X_5,not(X_5)) != or(not(X_5),not(X_5))
    | or(not(X_5),not(X_5)) = implies(X_5,not(X_5)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X_5,not(X_5)))),bind(Y0,$fot(or(not(X_5),not(X_5))))]]) ).

cnf(refute_0_8,plain,
    or(not(X_5),not(X_5)) = implies(X_5,not(X_5)),
    inference(resolve,[$cnf( $equal(implies(X_5,not(X_5)),or(not(X_5),not(X_5))) )],[refute_0_3,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( or(not(X_5),not(X_5)) != implies(X_5,not(X_5))
    | ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
    | theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
    introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) ),[0,0],$fot(implies(X_5,not(X_5)))]]) ).

cnf(refute_0_10,plain,
    ( ~ theorem(implies(or(not(X_5),not(X_5)),not(X_5)))
    | theorem(implies(implies(X_5,not(X_5)),not(X_5))) ),
    inference(resolve,[$cnf( $equal(or(not(X_5),not(X_5)),implies(X_5,not(X_5))) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    theorem(implies(implies(X_5,not(X_5)),not(X_5))),
    inference(resolve,[$cnf( theorem(implies(or(not(X_5),not(X_5)),not(X_5))) )],[refute_0_2,refute_0_10]) ).

cnf(refute_0_12,plain,
    theorem(implies(implies(p,not(p)),not(p))),
    inference(subst,[],[refute_0_11:[bind(X_5,$fot(p))]]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( theorem(implies(implies(p,not(p)),not(p))) )],[refute_0_12,prove_this]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL169-3 : TPTP v8.1.0. Released v2.3.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n019.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul  4 07:02:08 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  
% 0.14/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.35  
%------------------------------------------------------------------------------