%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE001+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 05:25:30 EDT 2023

% Result   : Theorem 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   20 (   6 unt;   8 typ;   0 def)
%            Number of atoms       :   20 (   7 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   14 (   6   ~;   3   |;   2   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   16 (   0 sgn;  12   !;   0   ?;   0   :)

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

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

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

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

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

tff(decl_27,type,
    esk1_0: $i ).

tff(decl_28,type,
    esk2_0: $i ).

tff(decl_29,type,
    esk3_0: $i ).

fof(goals,conjecture,
    ! [X4,X5,X6] :
      ( leq(X4,X5)
     => leq(addition(X4,X6),addition(X4,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(order,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).

fof(additive_idempotence,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X4,X5,X6] :
        ( leq(X4,X5)
       => leq(addition(X4,X6),addition(X4,X6)) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_4,plain,
    ! [X27,X28] :
      ( ( ~ leq(X27,X28)
        | addition(X27,X28) = X28 )
      & ( addition(X27,X28) != X28
        | leq(X27,X28) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).

fof(c_0_5,plain,
    ! [X13] : addition(X13,X13) = X13,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

fof(c_0_6,negated_conjecture,
    ( leq(esk1_0,esk2_0)
    & ~ leq(addition(esk1_0,esk3_0),addition(esk1_0,esk3_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ~ leq(addition(esk1_0,esk3_0),addition(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    leq(X1,X1),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE001+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 12:41:08 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.61  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.005000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.007000 s
%------------------------------------------------------------------------------