%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HEN009-2 : 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 : 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 01:54:23 EDT 2023

% Result   : Unsatisfiable 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   35 (  15 unt;   9 typ;   0 def)
%            Number of atoms       :   50 (   4 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   51 (  27   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    1 (   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    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   39 (   2 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,
    a: $i ).

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

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

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

cnf(xQyLEz_implies_xQzLEy,axiom,
    ( less_equal(X5,X2)
    | ~ quotient(X1,X2,X3)
    | ~ less_equal(X3,X4)
    | ~ quotient(X1,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).

cnf(identity_divide_idQ_idQa,hypothesis,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).

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

cnf(x_divde_zero_is_x,axiom,
    quotient(X1,zero,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).

cnf(identity_divide_idQa,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).

cnf(xLEy_implies_zQyLEzQx,axiom,
    ( less_equal(X4,X5)
    | ~ less_equal(X1,X2)
    | ~ quotient(X3,X2,X4)
    | ~ quotient(X3,X1,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).

cnf(identity_divide_a,hypothesis,
    quotient(identity,a,idQa),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).

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(prove_one_inversion_equals_three,negated_conjecture,
    idQa != idQ__idQ_idQa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_one_inversion_equals_three) ).

cnf(c_0_9,axiom,
    ( less_equal(X5,X2)
    | ~ quotient(X1,X2,X3)
    | ~ less_equal(X3,X4)
    | ~ quotient(X1,X4,X5) ),
    xQyLEz_implies_xQzLEy ).

cnf(c_0_10,hypothesis,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    identity_divide_idQ_idQa ).

cnf(c_0_11,axiom,
    ( less_equal(X3,X1)
    | ~ quotient(X1,X2,X3) ),
    divisor_existence ).

cnf(c_0_12,axiom,
    quotient(X1,zero,X1),
    x_divde_zero_is_x ).

cnf(c_0_13,hypothesis,
    quotient(identity,idQa,idQ_idQa),
    identity_divide_idQa ).

cnf(c_0_14,hypothesis,
    ( less_equal(idQ__idQ_idQa,X1)
    | ~ quotient(identity,X1,X2)
    | ~ less_equal(X2,idQ_idQa) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_15,plain,
    less_equal(X1,X1),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,axiom,
    ( less_equal(X4,X5)
    | ~ less_equal(X1,X2)
    | ~ quotient(X3,X2,X4)
    | ~ quotient(X3,X1,X5) ),
    xLEy_implies_zQyLEzQx ).

cnf(c_0_17,hypothesis,
    quotient(identity,a,idQa),
    identity_divide_a ).

cnf(c_0_18,hypothesis,
    ( less_equal(idQ_idQa,X1)
    | ~ quotient(identity,X1,X2)
    | ~ less_equal(X2,idQa) ),
    inference(spm,[status(thm)],[c_0_9,c_0_13]) ).

cnf(c_0_19,axiom,
    ( X1 = X2
    | ~ less_equal(X1,X2)
    | ~ less_equal(X2,X1) ),
    less_equal_and_equal ).

cnf(c_0_20,hypothesis,
    less_equal(idQ__idQ_idQa,idQa),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15])]) ).

cnf(c_0_21,negated_conjecture,
    idQa != idQ__idQ_idQa,
    prove_one_inversion_equals_three ).

cnf(c_0_22,hypothesis,
    ( less_equal(idQa,X1)
    | ~ quotient(identity,X2,X1)
    | ~ less_equal(X2,a) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,hypothesis,
    less_equal(idQ_idQa,a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_15])]) ).

cnf(c_0_24,hypothesis,
    ~ less_equal(idQa,idQ__idQ_idQa),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_25,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_10]),c_0_23])]),c_0_24]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : HEN009-2 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 13:00:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.008000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.011000 s
%------------------------------------------------------------------------------