%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN009-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 01:54:24 EDT 2023

% Result   : Unsatisfiable 0.18s 0.62s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   23 (   9 unt;   5 typ;   0 def)
%            Number of atoms       :   29 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  13   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (   5 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

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

cnf(property_of_divide3,axiom,
    ( less_equal(divide(X1,X3),divide(X2,X3))
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide3) ).

cnf(identity_is_largest,axiom,
    less_equal(X1,identity),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).

cnf(property_of_divide1,axiom,
    ( less_equal(divide(X1,X3),X2)
    | ~ less_equal(divide(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).

cnf(less_equal_and_equal,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).

cnf(property_of_divide2,axiom,
    ( less_equal(divide(X3,X2),divide(X3,X1))
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide2) ).

cnf(prove_this,negated_conjecture,
    divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

cnf(c_0_6,axiom,
    ( less_equal(divide(X1,X3),divide(X2,X3))
    | ~ less_equal(X1,X2) ),
    property_of_divide3 ).

cnf(c_0_7,axiom,
    less_equal(X1,identity),
    identity_is_largest ).

cnf(c_0_8,axiom,
    ( less_equal(divide(X1,X3),X2)
    | ~ less_equal(divide(X1,X2),X3) ),
    property_of_divide1 ).

cnf(c_0_9,plain,
    less_equal(divide(X1,X2),divide(identity,X2)),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_11,plain,
    less_equal(divide(X1,divide(identity,X2)),X2),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,axiom,
    ( less_equal(divide(X3,X2),divide(X3,X1))
    | ~ less_equal(X1,X2) ),
    property_of_divide2 ).

cnf(c_0_13,plain,
    ( divide(X1,divide(identity,X2)) = X2
    | ~ less_equal(X2,divide(X1,divide(identity,X2))) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    less_equal(divide(X1,X2),divide(X1,divide(X3,divide(identity,X2)))),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
    prove_this ).

cnf(c_0_16,plain,
    divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
    inference(spm,[status(thm)],[c_0_13,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
% 0.12/0.13  % Problem    : HEN009-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Thu Aug 24 13:25:22 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.18/0.58  start to proof: theBenchmark
% 0.18/0.62  % Version  : CSE_E---1.5
% 0.18/0.62  % Problem  : theBenchmark.p
% 0.18/0.62  % Proof found
% 0.18/0.62  % SZS status Theorem for theBenchmark.p
% 0.18/0.62  % SZS output start Proof
% See solution above
% 0.18/0.62  % Total time : 0.027000 s
% 0.18/0.62  % SZS output end Proof
% 0.18/0.62  % Total time : 0.030000 s
%------------------------------------------------------------------------------