TSTP Solution File: SET879+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 14:36:06 EDT 2023

% Result   : Theorem 0.13s 0.48s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   28 (   4 unt;   9 typ;   0 def)
%            Number of atoms       :   51 (  34 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   57 (  25   ~;  21   |;   5   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   32 (   0 sgn;  19   !;   0   ?;   0   :)

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

tff(decl_23,type,
    singleton: $i > $i ).

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

tff(decl_25,type,
    empty: $i > $o ).

tff(decl_26,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk2_0: $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

tff(decl_30,type,
    esk5_0: $i ).

fof(l34_zfmisc_1,axiom,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = singleton(X1)
    <=> ~ in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).

fof(t20_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
    <=> X1 != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(c_0_3,plain,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = singleton(X1)
    <=> ~ in(X1,X2) ),
    inference(fof_simplification,[status(thm)],[l34_zfmisc_1]) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
      <=> X1 != X2 ),
    inference(assume_negation,[status(cth)],[t20_zfmisc_1]) ).

fof(c_0_5,plain,
    ! [X6,X7,X8,X9,X10,X11] :
      ( ( ~ in(X8,X7)
        | X8 = X6
        | X7 != singleton(X6) )
      & ( X9 != X6
        | in(X9,X7)
        | X7 != singleton(X6) )
      & ( ~ in(esk1_2(X10,X11),X11)
        | esk1_2(X10,X11) != X10
        | X11 = singleton(X10) )
      & ( in(esk1_2(X10,X11),X11)
        | esk1_2(X10,X11) = X10
        | X11 = singleton(X10) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).

fof(c_0_6,plain,
    ! [X13,X14] :
      ( ( set_difference(singleton(X13),X14) != singleton(X13)
        | ~ in(X13,X14) )
      & ( in(X13,X14)
        | set_difference(singleton(X13),X14) = singleton(X13) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).

fof(c_0_7,negated_conjecture,
    ( ( set_difference(singleton(esk4_0),singleton(esk5_0)) != singleton(esk4_0)
      | esk4_0 = esk5_0 )
    & ( set_difference(singleton(esk4_0),singleton(esk5_0)) = singleton(esk4_0)
      | esk4_0 != esk5_0 ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

cnf(c_0_8,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( set_difference(singleton(X1),X2) != singleton(X1)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( set_difference(singleton(esk4_0),singleton(esk5_0)) = singleton(esk4_0)
    | esk4_0 != esk5_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ( esk4_0 = esk5_0
    | set_difference(singleton(esk4_0),singleton(esk5_0)) != singleton(esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( in(X1,X2)
    | set_difference(singleton(X1),X2) = singleton(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,negated_conjecture,
    ~ in(esk4_0,singleton(esk5_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_15,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,negated_conjecture,
    esk5_0 = esk4_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_17,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).

cnf(c_0_18,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.28  % Computer : n032.cluster.edu
% 0.11/0.28  % Model    : x86_64 x86_64
% 0.11/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28  % Memory   : 8042.1875MB
% 0.11/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29  % CPULimit   : 300
% 0.11/0.29  % WCLimit    : 300
% 0.11/0.29  % DateTime   : Sat Aug 26 13:17:14 EDT 2023
% 0.11/0.29  % CPUTime  : 
% 0.13/0.46  start to proof: theBenchmark
% 0.13/0.47  % Version  : CSE_E---1.5
% 0.13/0.47  % Problem  : theBenchmark.p
% 0.13/0.47  % Proof found
% 0.13/0.48  % SZS status Theorem for theBenchmark.p
% 0.13/0.48  % SZS output start Proof
% See solution above
% 0.13/0.48  % Total time : 0.005000 s
% 0.13/0.48  % SZS output end Proof
% 0.13/0.48  % Total time : 0.007000 s
%------------------------------------------------------------------------------