%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN007-4 : 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 : n005.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 01:54:21 EDT 2023

% Result   : Unsatisfiable 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   25 (  11 unt;   7 typ;   0 def)
%            Number of atoms       :   27 (   4 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  11   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   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    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   24 (   0 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 ).

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

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

cnf(quotient_less_equal2,axiom,
    ( less_equal(X1,X2)
    | divide(X1,X2) != zero ),
    file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).

cnf(x_divide_x_is_zero,axiom,
    divide(X1,X1) = zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).

cnf(transitivity_of_less_equal,axiom,
    ( less_equal(X1,X3)
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).

cnf(a_LE_b,hypothesis,
    less_equal(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).

cnf(property_of_divide1,axiom,
    ( less_equal(divide(X1,X3),X2)
    | ~ less_equal(divide(X1,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).

cnf(prove_c_divide_b_LE_c_divide_a,negated_conjecture,
    ~ less_equal(divide(c,b),divide(c,a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).

cnf(c_0_6,axiom,
    ( less_equal(X1,X2)
    | divide(X1,X2) != zero ),
    quotient_less_equal2 ).

cnf(c_0_7,axiom,
    divide(X1,X1) = zero,
    x_divide_x_is_zero ).

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

cnf(c_0_9,hypothesis,
    less_equal(a,b),
    a_LE_b ).

cnf(c_0_10,axiom,
    ( less_equal(divide(X1,X3),X2)
    | ~ less_equal(divide(X1,X2),X3) ),
    property_of_divide1 ).

cnf(c_0_11,plain,
    less_equal(X1,X1),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_12,hypothesis,
    ( less_equal(X1,b)
    | ~ less_equal(X1,a) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

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

cnf(c_0_14,hypothesis,
    less_equal(divide(X1,divide(X1,a)),b),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,negated_conjecture,
    ~ less_equal(divide(c,b),divide(c,a)),
    prove_c_divide_b_LE_c_divide_a ).

cnf(c_0_16,hypothesis,
    less_equal(divide(X1,b),divide(X1,a)),
    inference(spm,[status(thm)],[c_0_10,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
% 0.00/0.12  % Problem    : HEN007-4 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Thu Aug 24 13:19:38 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.57  % Total time : 0.009000 s
% 0.19/0.57  % SZS output end Proof
% 0.19/0.57  % Total time : 0.011000 s
%------------------------------------------------------------------------------