%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN003-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 01:54:15 EDT 2023

% Result   : Unsatisfiable 0.51s 0.65s
% Output   : CNFRefutation 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   20 (  13 unt;   4 typ;   0 def)
%            Number of atoms       :   21 (  20 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   12 (   7   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   23 (   5 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    zero: $i ).

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

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

cnf(quotient_property,axiom,
    divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',quotient_property) ).

cnf(quotient_smaller_than_numerator,axiom,
    divide(divide(X1,X2),X1) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',quotient_smaller_than_numerator) ).

cnf(divide_and_equal,axiom,
    ( X1 = X2
    | divide(X1,X2) != zero
    | divide(X2,X1) != zero ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',divide_and_equal) ).

cnf(zero_is_smallest,axiom,
    divide(zero,X1) = zero,
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN003-0.ax',zero_is_smallest) ).

cnf(prove_x_divide_x_is_zero,negated_conjecture,
    divide(a,a) != zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).

cnf(c_0_5,axiom,
    divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
    quotient_property ).

cnf(c_0_6,axiom,
    divide(divide(X1,X2),X1) = zero,
    quotient_smaller_than_numerator ).

cnf(c_0_7,axiom,
    ( X1 = X2
    | divide(X1,X2) != zero
    | divide(X2,X1) != zero ),
    divide_and_equal ).

cnf(c_0_8,plain,
    divide(divide(divide(X1,X1),divide(X2,X1)),zero) = zero,
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,axiom,
    divide(zero,X1) = zero,
    zero_is_smallest ).

cnf(c_0_10,plain,
    ( divide(X1,X2) = X1
    | divide(X1,divide(X1,X2)) != zero ),
    inference(spm,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_11,plain,
    divide(divide(divide(X1,X1),zero),zero) = zero,
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    divide(divide(X1,X1),zero) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11])]) ).

cnf(c_0_13,negated_conjecture,
    divide(a,a) != zero,
    prove_x_divide_x_is_zero ).

cnf(c_0_14,plain,
    divide(X1,X1) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_12]),c_0_12])]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : HEN003-5 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Thu Aug 24 13:03:09 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.21/0.63  start to proof: theBenchmark
% 0.51/0.65  % Version  : CSE_E---1.5
% 0.51/0.65  % Problem  : theBenchmark.p
% 0.51/0.65  % Proof found
% 0.51/0.65  % SZS status Theorem for theBenchmark.p
% 0.51/0.65  % SZS output start Proof
% See solution above
% 0.51/0.66  % Total time : 0.005000 s
% 0.51/0.66  % SZS output end Proof
% 0.51/0.66  % Total time : 0.007000 s
%------------------------------------------------------------------------------