%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LCL076-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 12:49:14 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   11 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :   17 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   12 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
    ( ~ is_a_theorem(implies(X,Y))
    | ~ is_a_theorem(X)
    | is_a_theorem(Y) ) ).

cnf(cn_49,axiom,
    is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) ).

cnf(extra_lemma,axiom,
    is_a_theorem(implies(not(not(X1)),X1)) ).

cnf(prove_cn_40,negated_conjecture,
    ~ is_a_theorem(implies(a,not(not(a)))) ).

cnf(refute_0_0,plain,
    is_a_theorem(implies(not(not(not(X_23))),not(X_23))),
    inference(subst,[],[extra_lemma:[bind(X1,$fot(not(X_23)))]]) ).

cnf(refute_0_1,plain,
    ( ~ is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))
    | ~ is_a_theorem(implies(not(X),not(Y)))
    | is_a_theorem(implies(Y,X)) ),
    inference(subst,[],[condensed_detachment:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).

cnf(refute_0_2,plain,
    ( ~ is_a_theorem(implies(not(X),not(Y)))
    | is_a_theorem(implies(Y,X)) ),
    inference(resolve,[$cnf( is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))) )],[cn_49,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( ~ is_a_theorem(implies(not(not(not(X_23))),not(X_23)))
    | is_a_theorem(implies(X_23,not(not(X_23)))) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(not(not(X_23)))),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_4,plain,
    is_a_theorem(implies(X_23,not(not(X_23)))),
    inference(resolve,[$cnf( is_a_theorem(implies(not(not(not(X_23))),not(X_23))) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    is_a_theorem(implies(a,not(not(a)))),
    inference(subst,[],[refute_0_4:[bind(X_23,$fot(a))]]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( is_a_theorem(implies(a,not(not(a)))) )],[refute_0_5,prove_cn_40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL076-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n004.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 : Mon Jul  4 06:29:07 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------