%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LAT035-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n013.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 05:59:17 EDT 2023

% Result   : Unsatisfiable 0.20s 0.56s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   19 (   9 unt;   8 typ;   0 def)
%            Number of atoms       :   13 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   4   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :    8 (   0 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,
    n0: $i ).

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

tff(decl_26,type,
    k: $i > $i ).

tff(decl_27,type,
    f: $i > $i ).

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

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

cnf(comp_join_hemimorphism,negated_conjecture,
    ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
    | f(k(n0)) != n0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comp_join_hemimorphism) ).

cnf(k_on_bottom,axiom,
    k(n0) = n1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_on_bottom) ).

cnf(f_on_top,axiom,
    f(n1) = n0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_top) ).

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

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

cnf(c_0_5,negated_conjecture,
    ( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
    | f(k(n0)) != n0 ),
    comp_join_hemimorphism ).

cnf(c_0_6,axiom,
    k(n0) = n1,
    k_on_bottom ).

cnf(c_0_7,axiom,
    f(n1) = n0,
    f_on_top ).

cnf(c_0_8,axiom,
    f(meet(X1,X2)) = join(f(X1),f(X2)),
    f_on_meet ).

cnf(c_0_9,axiom,
    k(join(X1,X2)) = meet(k(X1),k(X2)),
    k_on_join ).

cnf(c_0_10,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_5,c_0_6]),c_0_7]),c_0_8]),c_0_9])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT035-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n013.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 07:35:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.54  start to proof: theBenchmark
% 0.20/0.56  % Version  : CSE_E---1.5
% 0.20/0.56  % Problem  : theBenchmark.p
% 0.20/0.56  % Proof found
% 0.20/0.56  % SZS status Theorem for theBenchmark.p
% 0.20/0.56  % SZS output start Proof
% See solution above
% 0.20/0.56  % Total time : 0.003000 s
% 0.20/0.56  % SZS output end Proof
% 0.20/0.56  % Total time : 0.006000 s
%------------------------------------------------------------------------------