%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : COL056-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   19 (  13 unt;   0 nHn;  17 RR)
%            Number of literals    :   28 (  27 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(composer_exists,axiom,
    response(compose(X,Y),W) = response(X,response(Y,W)) ).

cnf(a_to_b_responds_c,hypothesis,
    response(a,b) = c ).

cnf(a_to_c_responds_b,hypothesis,
    response(a,c) = b ).

cnf(prove_there_exists_a_happy_bird,negated_conjecture,
    response(W,V) != V ).

cnf(refute_0_0,plain,
    response(compose(X_3,X_4),V) != V,
    inference(subst,[],[prove_there_exists_a_happy_bird:[bind(W,$fot(compose(X_3,X_4)))]]) ).

cnf(refute_0_1,plain,
    response(compose(X_3,X_4),V) = response(X_3,response(X_4,V)),
    inference(subst,[],[composer_exists:[bind(W,$fot(V)),bind(X,$fot(X_3)),bind(Y,$fot(X_4))]]) ).

cnf(refute_0_2,plain,
    ( response(X_3,response(X_4,V)) != V
    | response(compose(X_3,X_4),V) != response(X_3,response(X_4,V))
    | response(compose(X_3,X_4),V) = V ),
    introduced(tautology,[equality,[$cnf( $equal(response(compose(X_3,X_4),V),response(X_3,response(X_4,V))) ),[1],$fot(V)]]) ).

cnf(refute_0_3,plain,
    ( response(X_3,response(X_4,V)) != V
    | response(compose(X_3,X_4),V) = V ),
    inference(resolve,[$cnf( $equal(response(compose(X_3,X_4),V),response(X_3,response(X_4,V))) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    response(X_3,response(X_4,V)) != V,
    inference(resolve,[$cnf( $equal(response(compose(X_3,X_4),V),V) )],[refute_0_3,refute_0_0]) ).

cnf(refute_0_5,plain,
    response(X_6,response(a,b)) != b,
    inference(subst,[],[refute_0_4:[bind(V,$fot(b)),bind(X_3,$fot(X_6)),bind(X_4,$fot(a))]]) ).

cnf(refute_0_6,plain,
    ( response(X_6,c) != b
    | response(a,b) != c
    | response(X_6,response(a,b)) = b ),
    introduced(tautology,[equality,[$cnf( ~ $equal(response(X_6,response(a,b)),b) ),[0,1],$fot(c)]]) ).

cnf(refute_0_7,plain,
    ( response(X_6,c) != b
    | response(X_6,response(a,b)) = b ),
    inference(resolve,[$cnf( $equal(response(a,b),c) )],[a_to_b_responds_c,refute_0_6]) ).

cnf(refute_0_8,plain,
    response(X_6,c) != b,
    inference(resolve,[$cnf( $equal(response(X_6,response(a,b)),b) )],[refute_0_7,refute_0_5]) ).

cnf(refute_0_9,plain,
    response(a,c) != b,
    inference(subst,[],[refute_0_8:[bind(X_6,$fot(a))]]) ).

cnf(refute_0_10,plain,
    ( b != b
    | response(a,c) != b
    | response(a,c) = b ),
    introduced(tautology,[equality,[$cnf( $equal(response(a,c),b) ),[1],$fot(b)]]) ).

cnf(refute_0_11,plain,
    ( b != b
    | response(a,c) = b ),
    inference(resolve,[$cnf( $equal(response(a,c),b) )],[a_to_c_responds_b,refute_0_10]) ).

cnf(refute_0_12,plain,
    b != b,
    inference(resolve,[$cnf( $equal(response(a,c),b) )],[refute_0_11,refute_0_9]) ).

cnf(refute_0_13,plain,
    b = b,
    introduced(tautology,[refl,[$fot(b)]]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( $equal(b,b) )],[refute_0_13,refute_0_12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : COL056-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n023.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 : Tue May 31 12:17:11 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  
%------------------------------------------------------------------------------