%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN352-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 09:01:40 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   20 (   6 unt;   6 nHn;  15 RR)
%            Number of literals    :   38 (   0 equ;  17 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause1,negated_conjecture,
    f(a,b) ).

cnf(clause2,negated_conjecture,
    ( ~ f(X,Y)
    | f(b,z(X,Y))
    | f(Y,z(X,Y)) ) ).

cnf(clause3,negated_conjecture,
    ( f(X,Y)
    | f(z(X,Y),z(X,Y)) ) ).

cnf(clause6,negated_conjecture,
    ( ~ f(X,Y)
    | ~ f(X,z(X,Y))
    | ~ f(Y,z(X,Y)) ) ).

cnf(clause7,negated_conjecture,
    ( ~ f(X,Y)
    | f(X,z(X,Y))
    | f(Y,z(X,Y)) ) ).

cnf(refute_0_0,plain,
    ( ~ f(a,b)
    | f(b,z(a,b)) ),
    inference(subst,[],[clause2:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_1,plain,
    f(b,z(a,b)),
    inference(resolve,[$cnf( f(a,b) )],[clause1,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ f(a,b)
    | ~ f(a,z(a,b))
    | ~ f(b,z(a,b)) ),
    inference(subst,[],[clause6:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).

cnf(refute_0_3,plain,
    ( ~ f(a,b)
    | ~ f(a,z(a,b)) ),
    inference(resolve,[$cnf( f(b,z(a,b)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ~ f(a,z(a,b)),
    inference(resolve,[$cnf( f(a,b) )],[clause1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( f(X_12,X_13)
    | f(z(X_12,X_13),z(X_12,X_13)) ),
    inference(subst,[],[clause3:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_6,plain,
    ( ~ f(z(X_10,X_11),z(X_10,X_11))
    | ~ f(z(X_10,X_11),z(z(X_10,X_11),z(X_10,X_11))) ),
    inference(subst,[],[clause6:[bind(X,$fot(z(X_10,X_11))),bind(Y,$fot(z(X_10,X_11)))]]) ).

cnf(refute_0_7,plain,
    ( ~ f(z(X,Y),z(X,Y))
    | f(z(X,Y),z(z(X,Y),z(X,Y))) ),
    inference(subst,[],[clause7:[bind(X,$fot(z(X,Y))),bind(Y,$fot(z(X,Y)))]]) ).

cnf(refute_0_8,plain,
    ( f(X,Y)
    | f(z(X,Y),z(z(X,Y),z(X,Y))) ),
    inference(resolve,[$cnf( f(z(X,Y),z(X,Y)) )],[clause3,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( f(X_10,X_11)
    | f(z(X_10,X_11),z(z(X_10,X_11),z(X_10,X_11))) ),
    inference(subst,[],[refute_0_8:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).

cnf(refute_0_10,plain,
    ( ~ f(z(X_10,X_11),z(X_10,X_11))
    | f(X_10,X_11) ),
    inference(resolve,[$cnf( f(z(X_10,X_11),z(z(X_10,X_11),z(X_10,X_11))) )],[refute_0_9,refute_0_6]) ).

cnf(refute_0_11,plain,
    ( ~ f(z(X_12,X_13),z(X_12,X_13))
    | f(X_12,X_13) ),
    inference(subst,[],[refute_0_10:[bind(X_10,$fot(X_12)),bind(X_11,$fot(X_13))]]) ).

cnf(refute_0_12,plain,
    f(X_12,X_13),
    inference(resolve,[$cnf( f(z(X_12,X_13),z(X_12,X_13)) )],[refute_0_5,refute_0_11]) ).

cnf(refute_0_13,plain,
    f(a,z(a,b)),
    inference(subst,[],[refute_0_12:[bind(X_12,$fot(a)),bind(X_13,$fot(z(a,b)))]]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( f(a,z(a,b)) )],[refute_0_13,refute_0_4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN352-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n011.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 : Mon Jul 11 19:34:12 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  
%------------------------------------------------------------------------------