%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN008-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 01:54:22 EDT 2023

% Result   : Unsatisfiable 0.17s 0.55s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   28 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :   29 (  10 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   18 (  10   ~;   8   |;   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   :   25 (   4 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_equal1,axiom,
    ( divide(X1,X2) = zero
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).

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

cnf(quotient_property,axiom,
    less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).

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

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(zero_is_smallest,axiom,
    less_equal(zero,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).

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

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

cnf(c_0_8,axiom,
    ( divide(X1,X2) = zero
    | ~ less_equal(X1,X2) ),
    quotient_less_equal1 ).

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

cnf(c_0_10,axiom,
    less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)),
    quotient_property ).

cnf(c_0_11,hypothesis,
    divide(a,b) = zero,
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,axiom,
    divide(zero,X1) = zero,
    zero_divide_anything_is_zero ).

cnf(c_0_13,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_14,hypothesis,
    less_equal(divide(divide(a,X1),divide(b,X1)),zero),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).

cnf(c_0_15,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_16,axiom,
    ( less_equal(X1,X2)
    | divide(X1,X2) != zero ),
    quotient_less_equal2 ).

cnf(c_0_17,hypothesis,
    divide(divide(a,X1),divide(b,X1)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_18,negated_conjecture,
    ~ less_equal(divide(a,c),divide(b,c)),
    prove_a_divide_c_LE_b_divide_c ).

cnf(c_0_19,hypothesis,
    less_equal(divide(a,X1),divide(b,X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : HEN008-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32  % Computer : n020.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Thu Aug 24 13:23:45 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.17/0.53  start to proof: theBenchmark
% 0.17/0.55  % Version  : CSE_E---1.5
% 0.17/0.55  % Problem  : theBenchmark.p
% 0.17/0.55  % Proof found
% 0.17/0.55  % SZS status Theorem for theBenchmark.p
% 0.17/0.55  % SZS output start Proof
% See solution above
% 0.17/0.55  % Total time : 0.006000 s
% 0.17/0.55  % SZS output end Proof
% 0.17/0.55  % Total time : 0.009000 s
%------------------------------------------------------------------------------