%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 08:58:19 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   22 (  13 unt;   5 nHn;  13 RR)
%            Number of literals    :   34 (   0 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   28 (  15 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(clause_1,negated_conjecture,
    ( ~ p1(X,f(Y))
    | q1(f(X),Y)
    | q2(X,f(Y)) ) ).

cnf(clause_2,negated_conjecture,
    p1(a,Y) ).

cnf(clause_3,negated_conjecture,
    ~ q2(X,f(Y)) ).

cnf(clause_4,negated_conjecture,
    ( ~ p2(X,f(Y))
    | q3(f(X),Y)
    | q4(X,f(Y)) ) ).

cnf(clause_5,negated_conjecture,
    ~ q3(X,g(Y)) ).

cnf(clause_6,negated_conjecture,
    ~ q4(f(f(X)),f(g(f(Y)))) ).

cnf(clause_7,negated_conjecture,
    ( ~ q1(X,f(Y))
    | p2(f(X),Y) ) ).

cnf(refute_0_0,plain,
    ~ q4(f(f(a)),f(g(f(Y)))),
    inference(subst,[],[clause_6:[bind(X,$fot(a))]]) ).

cnf(refute_0_1,plain,
    p1(a,f(X_8)),
    inference(subst,[],[clause_2:[bind(Y,$fot(f(X_8)))]]) ).

cnf(refute_0_2,plain,
    ( ~ p1(X,f(Y))
    | q1(f(X),Y) ),
    inference(resolve,[$cnf( q2(X,f(Y)) )],[clause_1,clause_3]) ).

cnf(refute_0_3,plain,
    ( ~ p1(a,f(X_8))
    | q1(f(a),X_8) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(a)),bind(Y,$fot(X_8))]]) ).

cnf(refute_0_4,plain,
    q1(f(a),X_8),
    inference(resolve,[$cnf( p1(a,f(X_8)) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    q1(f(a),f(X_11)),
    inference(subst,[],[refute_0_4:[bind(X_8,$fot(f(X_11)))]]) ).

cnf(refute_0_6,plain,
    ( ~ q1(f(a),f(X_11))
    | p2(f(f(a)),X_11) ),
    inference(subst,[],[clause_7:[bind(X,$fot(f(a))),bind(Y,$fot(X_11))]]) ).

cnf(refute_0_7,plain,
    p2(f(f(a)),X_11),
    inference(resolve,[$cnf( q1(f(a),f(X_11)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    p2(f(f(a)),f(X_14)),
    inference(subst,[],[refute_0_7:[bind(X_11,$fot(f(X_14)))]]) ).

cnf(refute_0_9,plain,
    ( ~ p2(f(f(a)),f(X_14))
    | q3(f(f(f(a))),X_14)
    | q4(f(f(a)),f(X_14)) ),
    inference(subst,[],[clause_4:[bind(X,$fot(f(f(a)))),bind(Y,$fot(X_14))]]) ).

cnf(refute_0_10,plain,
    ( q3(f(f(f(a))),X_14)
    | q4(f(f(a)),f(X_14)) ),
    inference(resolve,[$cnf( p2(f(f(a)),f(X_14)) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( q3(f(f(f(a))),g(f(Y)))
    | q4(f(f(a)),f(g(f(Y)))) ),
    inference(subst,[],[refute_0_10:[bind(X_14,$fot(g(f(Y))))]]) ).

cnf(refute_0_12,plain,
    q3(f(f(f(a))),g(f(Y))),
    inference(resolve,[$cnf( q4(f(f(a)),f(g(f(Y)))) )],[refute_0_11,refute_0_0]) ).

cnf(refute_0_13,plain,
    ~ q3(f(f(f(a))),g(f(Y))),
    inference(subst,[],[clause_5:[bind(X,$fot(f(f(f(a))))),bind(Y,$fot(f(Y)))]]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( q3(f(f(f(a))),g(f(Y))) )],[refute_0_12,refute_0_13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11  % Problem  : SYN006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n027.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 Jul 12 06:02:19 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  
%------------------------------------------------------------------------------