%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN083-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 : Thu Jul 21 08:59:26 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   19 (  10 unt;   0 nHn;  16 RR)
%            Number of literals    :   33 (  32 equ;  16 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   20 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(f_is_associative,axiom,
    f(X,f(Y,Z)) = f(f(X,Y),Z) ).

cnf(prove_this,negated_conjecture,
    f(a,f(b,f(c,d))) != f(f(f(a,b),c),d) ).

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( f(X,f(Y,Z)) != f(f(X,Y),Z)
    | f(f(X,Y),Z) = f(X,f(Y,Z)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(f(X,f(Y,Z)))),bind(Y0,$fot(f(f(X,Y),Z)))]]) ).

cnf(refute_0_4,plain,
    f(f(X,Y),Z) = f(X,f(Y,Z)),
    inference(resolve,[$cnf( $equal(f(X,f(Y,Z)),f(f(X,Y),Z)) )],[f_is_associative,refute_0_3]) ).

cnf(refute_0_5,plain,
    f(f(a,b),f(c,d)) = f(a,f(b,f(c,d))),
    inference(subst,[],[refute_0_4:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(f(c,d)))]]) ).

cnf(refute_0_6,plain,
    f(f(f(a,b),c),d) = f(f(a,b),f(c,d)),
    inference(subst,[],[refute_0_4:[bind(X,$fot(f(a,b))),bind(Y,$fot(c)),bind(Z,$fot(d))]]) ).

cnf(refute_0_7,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_8,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( f(f(a,b),f(c,d)) != f(a,f(b,f(c,d)))
    | f(f(f(a,b),c),d) != f(f(a,b),f(c,d))
    | f(f(f(a,b),c),d) = f(a,f(b,f(c,d))) ),
    inference(subst,[],[refute_0_8:[bind(X0,$fot(f(f(f(a,b),c),d))),bind(Y0,$fot(f(f(a,b),f(c,d)))),bind(Z0,$fot(f(a,f(b,f(c,d)))))]]) ).

cnf(refute_0_10,plain,
    ( f(f(a,b),f(c,d)) != f(a,f(b,f(c,d)))
    | f(f(f(a,b),c),d) = f(a,f(b,f(c,d))) ),
    inference(resolve,[$cnf( $equal(f(f(f(a,b),c),d),f(f(a,b),f(c,d))) )],[refute_0_6,refute_0_9]) ).

cnf(refute_0_11,plain,
    f(f(f(a,b),c),d) = f(a,f(b,f(c,d))),
    inference(resolve,[$cnf( $equal(f(f(a,b),f(c,d)),f(a,f(b,f(c,d)))) )],[refute_0_5,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( f(a,f(b,f(c,d))) != f(a,f(b,f(c,d)))
    | f(f(f(a,b),c),d) != f(a,f(b,f(c,d)))
    | f(a,f(b,f(c,d))) = f(f(f(a,b),c),d) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(f(a,f(b,f(c,d))),f(f(f(a,b),c),d)) ),[1],$fot(f(a,f(b,f(c,d))))]]) ).

cnf(refute_0_13,plain,
    ( f(a,f(b,f(c,d))) != f(a,f(b,f(c,d)))
    | f(a,f(b,f(c,d))) = f(f(f(a,b),c),d) ),
    inference(resolve,[$cnf( $equal(f(f(f(a,b),c),d),f(a,f(b,f(c,d)))) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    f(a,f(b,f(c,d))) != f(a,f(b,f(c,d))),
    inference(resolve,[$cnf( $equal(f(a,f(b,f(c,d))),f(f(f(a,b),c),d)) )],[refute_0_13,prove_this]) ).

cnf(refute_0_15,plain,
    f(a,f(b,f(c,d))) = f(a,f(b,f(c,d))),
    introduced(tautology,[refl,[$fot(f(a,f(b,f(c,d))))]]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( $equal(f(a,f(b,f(c,d))),f(a,f(b,f(c,d)))) )],[refute_0_15,refute_0_14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SYN083-1 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n024.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 11 14:14:28 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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  
%------------------------------------------------------------------------------