%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : FLD065-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n001.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 : Wed Aug 30 22:27:46 EDT 2023

% Result   : Unsatisfiable 0.22s 0.63s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   27 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :   28 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   26 (  14   ~;  12   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    additive_inverse: $i > $i ).

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

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

tff(decl_28,type,
    multiplicative_inverse: $i > $i ).

tff(decl_29,type,
    add: ( $i * $i ) > $i ).

tff(decl_30,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_31,type,
    less_or_equal: ( $i * $i ) > $o ).

tff(decl_32,type,
    a: $i ).

cnf(existence_of_identity_addition,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).

cnf(compatibility_of_order_relation_and_addition,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,X4)
    | ~ sum(X3,X5,X1)
    | ~ sum(X4,X5,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).

cnf(less_or_equal_2,negated_conjecture,
    less_or_equal(additive_inverse(a),additive_identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).

cnf(not_less_or_equal_3,negated_conjecture,
    ~ less_or_equal(additive_identity,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).

cnf(c_0_6,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_7,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_8,axiom,
    ( less_or_equal(X1,X2)
    | ~ less_or_equal(X3,X4)
    | ~ sum(X3,X5,X1)
    | ~ sum(X4,X5,X2) ),
    compatibility_of_order_relation_and_addition ).

cnf(c_0_9,hypothesis,
    sum(additive_identity,a,a),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_11,hypothesis,
    ( less_or_equal(X1,a)
    | ~ less_or_equal(X2,additive_identity)
    | ~ sum(X2,a,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,hypothesis,
    sum(additive_inverse(a),a,additive_identity),
    inference(spm,[status(thm)],[c_0_10,c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    less_or_equal(additive_inverse(a),additive_identity),
    less_or_equal_2 ).

cnf(c_0_14,negated_conjecture,
    ~ less_or_equal(additive_identity,a),
    not_less_or_equal_3 ).

cnf(c_0_15,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : FLD065-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.37  % Computer : n001.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Mon Aug 28 01:07:19 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.22/0.61  start to proof: theBenchmark
% 0.22/0.63  % Version  : CSE_E---1.5
% 0.22/0.63  % Problem  : theBenchmark.p
% 0.22/0.63  % Proof found
% 0.22/0.63  % SZS status Theorem for theBenchmark.p
% 0.22/0.63  % SZS output start Proof
% See solution above
% 0.22/0.63  % Total time : 0.008000 s
% 0.22/0.63  % SZS output end Proof
% 0.22/0.63  % Total time : 0.011000 s
%------------------------------------------------------------------------------