%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT042-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 05:59:19 EDT 2023

% Result   : Unsatisfiable 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   27 (  19 unt;   8 typ;   0 def)
%            Number of atoms       :   19 (  18 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   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  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   38 (   6 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,
    complement: $i > $i ).

tff(decl_25,type,
    n1: $i ).

tff(decl_26,type,
    n0: $i ).

tff(decl_27,type,
    a: $i ).

tff(decl_28,type,
    b: $i ).

tff(decl_29,type,
    c: $i ).

cnf(absorption2,axiom,
    join(X1,meet(X1,X2)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).

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

cnf(associativity_of_join,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).

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

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

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

cnf(c_0_6,axiom,
    join(X1,meet(X1,X2)) = X1,
    absorption2 ).

cnf(c_0_7,axiom,
    meet(X1,X2) = meet(X2,X1),
    commutativity_of_meet ).

cnf(c_0_8,axiom,
    join(join(X1,X2),X3) = join(X1,join(X2,X3)),
    associativity_of_join ).

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

cnf(c_0_10,plain,
    join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,axiom,
    meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
    distributivity ).

cnf(c_0_12,negated_conjecture,
    join(a,meet(b,join(a,c))) != meet(join(a,b),join(a,c)),
    prove_modular_law ).

cnf(c_0_13,plain,
    join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X2,X3)),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X1,X3)),
    inference(spm,[status(thm)],[c_0_11,c_0_7]) ).

cnf(c_0_15,axiom,
    meet(X1,join(X1,X2)) = X1,
    absorption1 ).

cnf(c_0_16,negated_conjecture,
    meet(join(a,b),join(a,c)) != join(a,meet(b,c)),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_7]),c_0_13]),c_0_7])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : LAT042-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Thu Aug 24 04:15:41 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.62  % SZS output start Proof
% See solution above
% 0.20/0.62  % Total time : 0.039000 s
% 0.20/0.62  % SZS output end Proof
% 0.20/0.62  % Total time : 0.041000 s
%------------------------------------------------------------------------------