%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT008-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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  : 300s
% DateTime : Thu Aug 31 05:59:07 EDT 2023

% Result   : Unsatisfiable 0.21s 0.60s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   22 (  18 unt;   4 typ;   0 def)
%            Number of atoms       :   18 (  17 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   34 (   6 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    join: ( $i * $i ) > $i ).

tff(decl_23,type,
    meet: ( $i * $i ) > $i ).

tff(decl_24,type,
    a: $i ).

tff(decl_25,type,
    b: $i ).

cnf(absorption,axiom,
    meet(X1,join(X1,X2)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption) ).

cnf(distribution,axiom,
    meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribution) ).

cnf(prove_absorbtion_dual,negated_conjecture,
    join(a,meet(a,b)) != a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion_dual) ).

cnf(c_0_3,axiom,
    meet(X1,join(X1,X2)) = X1,
    absorption ).

cnf(c_0_4,axiom,
    meet(X1,join(X2,X3)) = join(meet(X3,X1),meet(X2,X1)),
    distribution ).

cnf(c_0_5,plain,
    meet(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X1,X2),
    inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

cnf(c_0_6,plain,
    meet(meet(X1,X2),X2) = meet(X1,X2),
    inference(spm,[status(thm)],[c_0_5,c_0_3]) ).

cnf(c_0_7,plain,
    meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_6]),c_0_4]) ).

cnf(c_0_8,plain,
    meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_6]),c_0_4]) ).

cnf(c_0_9,plain,
    meet(X1,meet(X1,join(X2,X3))) = meet(X1,join(X3,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_4]),c_0_8]) ).

cnf(c_0_10,plain,
    meet(X1,join(X2,X1)) = meet(X1,X1),
    inference(spm,[status(thm)],[c_0_9,c_0_3]) ).

cnf(c_0_11,plain,
    meet(X1,X1) = X1,
    inference(spm,[status(thm)],[c_0_3,c_0_10]) ).

cnf(c_0_12,plain,
    join(X1,meet(X2,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_11]),c_0_10]),c_0_11]) ).

cnf(c_0_13,plain,
    join(X1,X1) = X1,
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_14,plain,
    meet(X1,X2) = meet(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_13]),c_0_13]) ).

cnf(c_0_15,negated_conjecture,
    join(a,meet(a,b)) != a,
    prove_absorbtion_dual ).

cnf(c_0_16,plain,
    join(X1,meet(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_12,c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : LAT008-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Thu Aug 24 09:03:32 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 0.21/0.60  % Version  : CSE_E---1.5
% 0.21/0.60  % Problem  : theBenchmark.p
% 0.21/0.60  % Proof found
% 0.21/0.60  % SZS status Theorem for theBenchmark.p
% 0.21/0.60  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.005000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.008000 s
%------------------------------------------------------------------------------