%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT039-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 05:59:18 EDT 2023

% Result   : Unsatisfiable 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   22 (  17 unt;   5 typ;   0 def)
%            Number of atoms       :   17 (  16 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    :    3 (   1 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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   21 (   3 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    zz: $i ).

cnf(absorption1,axiom,
    meet(X1,join(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).

cnf(commutativity_of_join,axiom,
    join(X1,X2) = join(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).

cnf(lhs,hypothesis,
    join(xx,yy) = yy,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs) ).

cnf(commutativity_of_meet,axiom,
    meet(X1,X2) = meet(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).

cnf(dist_meet,hypothesis,
    meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_meet) ).

cnf(rhs,negated_conjecture,
    join(xx,meet(yy,zz)) != meet(yy,join(xx,zz)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).

cnf(c_0_6,axiom,
    meet(X1,join(X1,X2)) = X1,
    absorption1 ).

cnf(c_0_7,axiom,
    join(X1,X2) = join(X2,X1),
    commutativity_of_join ).

cnf(c_0_8,hypothesis,
    join(xx,yy) = yy,
    lhs ).

cnf(c_0_9,plain,
    meet(X1,join(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,hypothesis,
    join(yy,xx) = yy,
    inference(rw,[status(thm)],[c_0_8,c_0_7]) ).

cnf(c_0_11,axiom,
    meet(X1,X2) = meet(X2,X1),
    commutativity_of_meet ).

cnf(c_0_12,hypothesis,
    meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
    dist_meet ).

cnf(c_0_13,hypothesis,
    meet(yy,xx) = xx,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    join(xx,meet(yy,zz)) != meet(yy,join(xx,zz)),
    rhs ).

cnf(c_0_15,hypothesis,
    meet(yy,join(xx,X1)) = join(xx,meet(yy,X1)),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT039-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n016.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    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 10:04:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.20/0.57  % Version  : CSE_E---1.5
% 0.20/0.57  % Problem  : theBenchmark.p
% 0.20/0.57  % Proof found
% 0.20/0.57  % SZS status Theorem for theBenchmark.p
% 0.20/0.57  % SZS output start Proof
% See solution above
% 0.20/0.57  % Total time : 0.007000 s
% 0.20/0.57  % SZS output end Proof
% 0.20/0.57  % Total time : 0.010000 s
%------------------------------------------------------------------------------