%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN006-2 : 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 : n031.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 01:54:19 EDT 2023

% Result   : Unsatisfiable 0.99s 1.06s
% Output   : CNFRefutation 0.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   45 (  18 unt;  10 typ;   0 def)
%            Number of atoms       :   73 (   3 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   78 (  40   ~;  38   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   71 (   6 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    quotient: ( $i * $i * $i ) > $o ).

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

tff(decl_26,type,
    divide: ( $i * $i ) > $i ).

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

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

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

tff(decl_30,type,
    z: $i ).

tff(decl_31,type,
    xQz: $i ).

cnf(quotient_property,axiom,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_property) ).

cnf(closure,axiom,
    quotient(X1,X2,divide(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',closure) ).

cnf(quotient_less_equal,axiom,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',quotient_less_equal) ).

cnf(xQz,hypothesis,
    quotient(x,z,xQz),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).

cnf(xQy,hypothesis,
    quotient(x,y,xQy),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQy) ).

cnf(xQyLEz,hypothesis,
    less_equal(xQy,z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz) ).

cnf(less_equal_and_equal,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_and_equal) ).

cnf(zero_is_smallest,axiom,
    less_equal(zero,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',zero_is_smallest) ).

cnf(divisor_existence,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',divisor_existence) ).

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

cnf(less_equal_quotient,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    file('/export/starexec/sandbox/benchmark/Axioms/HEN001-0.ax',less_equal_quotient) ).

cnf(prove_xQzLEy,negated_conjecture,
    ~ less_equal(xQz,y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xQzLEy) ).

cnf(c_0_12,axiom,
    ( less_equal(X7,X8)
    | ~ quotient(X1,X2,X3)
    | ~ quotient(X2,X4,X5)
    | ~ quotient(X1,X4,X6)
    | ~ quotient(X6,X5,X7)
    | ~ quotient(X3,X4,X8) ),
    quotient_property ).

cnf(c_0_13,axiom,
    quotient(X1,X2,divide(X1,X2)),
    closure ).

cnf(c_0_14,plain,
    ( less_equal(divide(X1,X2),X3)
    | ~ quotient(X4,X5,X3)
    | ~ quotient(X6,X5,X2)
    | ~ quotient(X7,X5,X1)
    | ~ quotient(X7,X6,X4) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,axiom,
    ( quotient(X1,X2,zero)
    | ~ less_equal(X1,X2) ),
    quotient_less_equal ).

cnf(c_0_16,plain,
    ( less_equal(divide(X1,X2),zero)
    | ~ quotient(X3,X4,X2)
    | ~ quotient(X5,X4,X1)
    | ~ quotient(X5,X3,X6)
    | ~ less_equal(X6,X4) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,plain,
    ( less_equal(divide(X1,divide(X2,X3)),zero)
    | ~ quotient(X4,X3,X1)
    | ~ quotient(X4,X2,X5)
    | ~ less_equal(X5,X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_13]) ).

cnf(c_0_18,hypothesis,
    quotient(x,z,xQz),
    xQz ).

cnf(c_0_19,hypothesis,
    ( less_equal(divide(xQz,divide(X1,z)),zero)
    | ~ quotient(x,X1,X2)
    | ~ less_equal(X2,z) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_20,hypothesis,
    quotient(x,y,xQy),
    xQy ).

cnf(c_0_21,hypothesis,
    less_equal(xQy,z),
    xQyLEz ).

cnf(c_0_22,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_23,hypothesis,
    less_equal(divide(xQz,divide(y,z)),zero),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_24,axiom,
    less_equal(zero,X1),
    zero_is_smallest ).

cnf(c_0_25,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    divisor_existence ).

cnf(c_0_26,hypothesis,
    divide(xQz,divide(y,z)) = zero,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_27,axiom,
    ( less_equal(X1,X3)
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X3) ),
    transitivity_of_less_equal ).

cnf(c_0_28,plain,
    less_equal(divide(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_13]) ).

cnf(c_0_29,axiom,
    ( less_equal(X1,X2)
    | ~ quotient(X1,X2,zero) ),
    less_equal_quotient ).

cnf(c_0_30,hypothesis,
    quotient(xQz,divide(y,z),zero),
    inference(spm,[status(thm)],[c_0_13,c_0_26]) ).

cnf(c_0_31,plain,
    ( less_equal(X1,X2)
    | ~ less_equal(X1,divide(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,hypothesis,
    less_equal(xQz,divide(y,z)),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_33,negated_conjecture,
    ~ less_equal(xQz,y),
    prove_xQzLEy ).

cnf(c_0_34,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : HEN006-2 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n031.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Thu Aug 24 13:46:51 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.99/1.06  % Version  : CSE_E---1.5
% 0.99/1.06  % Problem  : theBenchmark.p
% 0.99/1.06  % Proof found
% 0.99/1.06  % SZS status Theorem for theBenchmark.p
% 0.99/1.06  % SZS output start Proof
% See solution above
% 0.99/1.06  % Total time : 0.484000 s
% 0.99/1.06  % SZS output end Proof
% 0.99/1.06  % Total time : 0.486000 s
%------------------------------------------------------------------------------