TSTP Solution File: SET900+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET900+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 14:36:11 EDT 2023

% Result   : Theorem 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   21 (   3 unt;   9 typ;   0 def)
%            Number of atoms       :   35 (  27 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   47 (  24   ~;  11   |;  12   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn;  12   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    empty: $i > $o ).

tff(decl_25,type,
    singleton: $i > $i ).

tff(decl_26,type,
    esk1_0: $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_2: ( $i * $i ) > $i ).

fof(t41_zfmisc_1,conjecture,
    ! [X1,X2] :
      ~ ( X1 != singleton(X2)
        & X1 != empty_set
        & ! [X3] :
            ~ ( in(X3,X1)
              & X3 != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).

fof(l45_zfmisc_1,axiom,
    ! [X1,X2] :
      ~ ( X1 != singleton(X2)
        & X1 != empty_set
        & ! [X3] :
            ~ ( in(X3,X1)
              & X3 != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_zfmisc_1) ).

fof(c_0_2,negated_conjecture,
    ~ ! [X1,X2] :
        ~ ( X1 != singleton(X2)
          & X1 != empty_set
          & ! [X3] :
              ~ ( in(X3,X1)
                & X3 != X2 ) ),
    inference(assume_negation,[status(cth)],[t41_zfmisc_1]) ).

fof(c_0_3,negated_conjecture,
    ! [X10] :
      ( esk3_0 != singleton(esk4_0)
      & esk3_0 != empty_set
      & ( ~ in(X10,esk3_0)
        | X10 = esk4_0 ) ),
    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,X12] :
      ( ( in(esk5_2(X11,X12),X11)
        | X11 = singleton(X12)
        | X11 = empty_set )
      & ( esk5_2(X11,X12) != X12
        | X11 = singleton(X12)
        | X11 = empty_set ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_zfmisc_1])])])]) ).

cnf(c_0_5,negated_conjecture,
    ( X1 = esk4_0
    | ~ in(X1,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_6,plain,
    ( in(esk5_2(X1,X2),X1)
    | X1 = singleton(X2)
    | X1 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    esk3_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_8,plain,
    ( X1 = singleton(X2)
    | X1 = empty_set
    | esk5_2(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_9,negated_conjecture,
    ( esk5_2(esk3_0,X1) = esk4_0
    | singleton(X1) = esk3_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    esk3_0 != singleton(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_3]) ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_7])]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET900+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.33  % Computer : n016.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Sat Aug 26 10:29:11 EDT 2023
% 0.15/0.33  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.20/0.57  % Version  : CSE_E---1.5
% 0.20/0.57  % Problem  : theBenchmark.p
% 0.20/0.57  % Proof found
% 0.20/0.57  % SZS status Theorem for theBenchmark.p
% 0.20/0.57  % SZS output start Proof
% See solution above
% 0.20/0.57  % Total time : 0.006000 s
% 0.20/0.57  % SZS output end Proof
% 0.20/0.57  % Total time : 0.008000 s
%------------------------------------------------------------------------------