%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU139+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 16:22:41 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   23 (   9 unt;   4 typ;   0 def)
%            Number of atoms       :   36 (   5 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   37 (  20   ~;   8   |;   6   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   24 (   2 sgn;  19   !;   0   ?;   0   :)

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

tff(decl_23,type,
    subset: ( $i * $i ) > $o ).

tff(decl_24,type,
    esk1_0: $i ).

tff(decl_25,type,
    esk2_0: $i ).

fof(antisymmetry_r2_xboole_0,axiom,
    ! [X1,X2] :
      ( proper_subset(X1,X2)
     => ~ proper_subset(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).

fof(t60_xboole_1,conjecture,
    ! [X1,X2] :
      ~ ( subset(X1,X2)
        & proper_subset(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).

fof(d8_xboole_0,axiom,
    ! [X1,X2] :
      ( proper_subset(X1,X2)
    <=> ( subset(X1,X2)
        & X1 != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).

fof(irreflexivity_r2_xboole_0,axiom,
    ! [X1,X2] : ~ proper_subset(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).

fof(c_0_4,plain,
    ! [X1,X2] :
      ( proper_subset(X1,X2)
     => ~ proper_subset(X2,X1) ),
    inference(fof_simplification,[status(thm)],[antisymmetry_r2_xboole_0]) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2] :
        ~ ( subset(X1,X2)
          & proper_subset(X2,X1) ),
    inference(assume_negation,[status(cth)],[t60_xboole_1]) ).

fof(c_0_6,plain,
    ! [X3,X4] :
      ( ~ proper_subset(X3,X4)
      | ~ proper_subset(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

fof(c_0_7,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & proper_subset(esk2_0,esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_8,plain,
    ! [X7,X8] :
      ( ( subset(X7,X8)
        | ~ proper_subset(X7,X8) )
      & ( X7 != X8
        | ~ proper_subset(X7,X8) )
      & ( ~ subset(X7,X8)
        | X7 = X8
        | proper_subset(X7,X8) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).

cnf(c_0_9,plain,
    ( ~ proper_subset(X1,X2)
    | ~ proper_subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    proper_subset(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X1,X2] : ~ proper_subset(X1,X1),
    inference(fof_simplification,[status(thm)],[irreflexivity_r2_xboole_0]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | proper_subset(X1,X2)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_14,negated_conjecture,
    ~ proper_subset(esk1_0,esk2_0),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

fof(c_0_15,plain,
    ! [X9] : ~ proper_subset(X9,X9),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_11])]) ).

cnf(c_0_16,negated_conjecture,
    esk1_0 = esk2_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_17,plain,
    ~ proper_subset(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_16]),c_0_17]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU139+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n004.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   : Wed Aug 23 16:43:38 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.006000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.009000 s
%------------------------------------------------------------------------------