%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COL055-1 : 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 : Fri Jul 15 00:36:19 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   8 RR)
%            Number of literals    :   12 (  11 equ;   7 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    5 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(fond_bird_exists,hypothesis,
    response(a,b) = b ).

cnf(prove_happiness,negated_conjecture,
    ( response(a,Z) != W
    | response(a,W) != Z ) ).

cnf(refute_0_0,plain,
    ( response(a,W) != response(a,W)
    | response(a,response(a,W)) != W ),
    inference(subst,[],[prove_happiness:[bind(W,$fot(response(a,W))),bind(Z,$fot(W))]]) ).

cnf(refute_0_1,plain,
    response(a,W) = response(a,W),
    introduced(tautology,[refl,[$fot(response(a,W))]]) ).

cnf(refute_0_2,plain,
    response(a,response(a,W)) != W,
    inference(resolve,[$cnf( $equal(response(a,W),response(a,W)) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    response(a,response(a,b)) != b,
    inference(subst,[],[refute_0_2:[bind(W,$fot(b))]]) ).

cnf(refute_0_4,plain,
    ( response(a,b) != b
    | response(a,response(a,b)) = b ),
    introduced(tautology,[equality,[$cnf( ~ $equal(response(a,response(a,b)),b) ),[0,1],$fot(b)]]) ).

cnf(refute_0_5,plain,
    response(a,response(a,b)) = b,
    inference(resolve,[$cnf( $equal(response(a,b),b) )],[fond_bird_exists,refute_0_4]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( $equal(response(a,response(a,b)),b) )],[refute_0_5,refute_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : COL055-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n029.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 : Tue May 31 06:13:44 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34  
%------------------------------------------------------------------------------