%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE003+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n014.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 05:25:31 EDT 2023

% Result   : Theorem 0.22s 0.59s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   14 (   4 unt;   6 typ;   0 def)
%            Number of atoms       :   14 (  13 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   11 (   5   ~;   3   |;   1   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    6 (   0 sgn;   5   !;   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 ).

fof(goals,conjecture,
    ( ! [X4] : addition(X4,X4) = X4
  <=> addition(one,one) = one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

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

fof(c_0_2,negated_conjecture,
    ~ ( ! [X4] : addition(X4,X4) = X4
    <=> addition(one,one) = one ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_3,negated_conjecture,
    ! [X28] :
      ( ( addition(esk1_0,esk1_0) != esk1_0
        | addition(one,one) != one )
      & ( addition(X28,X28) = X28
        | addition(one,one) = one ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).

fof(c_0_4,plain,
    ! [X11] : addition(X11,X11) = X11,
    inference(variable_rename,[status(thm)],[additive_idempotence]) ).

cnf(c_0_5,negated_conjecture,
    ( addition(esk1_0,esk1_0) != esk1_0
    | addition(one,one) != one ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,plain,
    addition(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_6])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE003+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 29 11:49:45 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.22/0.57  start to proof: theBenchmark
% 0.22/0.59  % Version  : CSE_E---1.5
% 0.22/0.59  % Problem  : theBenchmark.p
% 0.22/0.59  % Proof found
% 0.22/0.59  % SZS status Theorem for theBenchmark.p
% 0.22/0.59  % SZS output start Proof
% See solution above
% 0.22/0.59  % Total time : 0.004000 s
% 0.22/0.59  % SZS output end Proof
% 0.22/0.59  % Total time : 0.006000 s
%------------------------------------------------------------------------------