%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : KLE059+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 05:25:54 EDT 2023

% Result   : Theorem 0.22s 0.61s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   17 (   6 unt;   8 typ;   0 def)
%            Number of atoms       :   12 (  11 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   3   ~;   0   |;   1   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   10 (   0 sgn;   8   !;   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,
    domain: $i > $i ).

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_0: $i ).

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

fof(domain5,axiom,
    ! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
    file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).

fof(c_0_2,negated_conjecture,
    ~ ! [X4,X5] :
        ( addition(X4,X5) = X5
       => addition(domain(X4),domain(X5)) = domain(X5) ),
    inference(assume_negation,[status(cth)],[goals]) ).

fof(c_0_3,negated_conjecture,
    ( addition(esk1_0,esk2_0) = esk2_0
    & addition(domain(esk1_0),domain(esk2_0)) != domain(esk2_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

fof(c_0_4,plain,
    ! [X32,X33] : domain(addition(X32,X33)) = addition(domain(X32),domain(X33)),
    inference(variable_rename,[status(thm)],[domain5]) ).

cnf(c_0_5,negated_conjecture,
    addition(domain(esk1_0),domain(esk2_0)) != domain(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,plain,
    domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    addition(esk1_0,esk2_0) = esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_8,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_6]),c_0_7])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : KLE059+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
% 0.15/0.35  % Computer : n014.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Aug 29 11:05:15 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.22/0.59  start to proof: theBenchmark
% 0.22/0.61  % Version  : CSE_E---1.5
% 0.22/0.61  % Problem  : theBenchmark.p
% 0.22/0.61  % Proof found
% 0.22/0.61  % SZS status Theorem for theBenchmark.p
% 0.22/0.61  % SZS output start Proof
% See solution above
% 0.22/0.61  % Total time : 0.005000 s
% 0.22/0.61  % SZS output end Proof
% 0.22/0.61  % Total time : 0.008000 s
%------------------------------------------------------------------------------