TSTP Solution File: SYN374+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SYN374+1 : TPTP v5.0.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 13:18:02 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   41 (   6 unt;   0 def)
%            Number of atoms       :  197 (   0 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  241 (  85   ~; 121   |;  27   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   3 prp; 0-1 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :   92 (  35 sgn  36   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ( ? [X1] :
      ! [X2] :
        ( big_p(X1)
      <=> big_p(X2) )
  <=> ( ? [X1] : big_p(X1)
    <=> ! [X2] : big_p(X2) ) ),
    file('/tmp/tmpJ3R9bm/sel_SYN374+1.p_1',x2125) ).

fof(2,negated_conjecture,
    ~ ( ? [X1] :
        ! [X2] :
          ( big_p(X1)
        <=> big_p(X2) )
    <=> ( ? [X1] : big_p(X1)
      <=> ! [X2] : big_p(X2) ) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(3,negated_conjecture,
    ( ( ! [X1] :
        ? [X2] :
          ( ( ~ big_p(X1)
            | ~ big_p(X2) )
          & ( big_p(X1)
            | big_p(X2) ) )
      | ( ( ! [X1] : ~ big_p(X1)
          | ? [X2] : ~ big_p(X2) )
        & ( ? [X1] : big_p(X1)
          | ! [X2] : big_p(X2) ) ) )
    & ( ? [X1] :
        ! [X2] :
          ( ( ~ big_p(X1)
            | big_p(X2) )
          & ( ~ big_p(X2)
            | big_p(X1) ) )
      | ( ( ! [X1] : ~ big_p(X1)
          | ! [X2] : big_p(X2) )
        & ( ? [X2] : ~ big_p(X2)
          | ? [X1] : big_p(X1) ) ) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(4,negated_conjecture,
    ( ( ! [X3] :
        ? [X4] :
          ( ( ~ big_p(X3)
            | ~ big_p(X4) )
          & ( big_p(X3)
            | big_p(X4) ) )
      | ( ( ! [X5] : ~ big_p(X5)
          | ? [X6] : ~ big_p(X6) )
        & ( ? [X7] : big_p(X7)
          | ! [X8] : big_p(X8) ) ) )
    & ( ? [X9] :
        ! [X10] :
          ( ( ~ big_p(X9)
            | big_p(X10) )
          & ( ~ big_p(X10)
            | big_p(X9) ) )
      | ( ( ! [X11] : ~ big_p(X11)
          | ! [X12] : big_p(X12) )
        & ( ? [X13] : ~ big_p(X13)
          | ? [X14] : big_p(X14) ) ) ) ),
    inference(variable_rename,[status(thm)],[3]) ).

fof(5,negated_conjecture,
    ( ( ! [X3] :
          ( ( ~ big_p(X3)
            | ~ big_p(esk1_1(X3)) )
          & ( big_p(X3)
            | big_p(esk1_1(X3)) ) )
      | ( ( ! [X5] : ~ big_p(X5)
          | ~ big_p(esk2_0) )
        & ( big_p(esk3_0)
          | ! [X8] : big_p(X8) ) ) )
    & ( ! [X10] :
          ( ( ~ big_p(esk4_0)
            | big_p(X10) )
          & ( ~ big_p(X10)
            | big_p(esk4_0) ) )
      | ( ( ! [X11] : ~ big_p(X11)
          | ! [X12] : big_p(X12) )
        & ( ~ big_p(esk5_0)
          | big_p(esk6_0) ) ) ) ),
    inference(skolemize,[status(esa)],[4]) ).

fof(6,negated_conjecture,
    ! [X3,X5,X8,X10,X11,X12] :
      ( ( ( ( big_p(X12)
            | ~ big_p(X11) )
          & ( ~ big_p(esk5_0)
            | big_p(esk6_0) ) )
        | ( ( ~ big_p(esk4_0)
            | big_p(X10) )
          & ( ~ big_p(X10)
            | big_p(esk4_0) ) ) )
      & ( ( ( big_p(X8)
            | big_p(esk3_0) )
          & ( ~ big_p(X5)
            | ~ big_p(esk2_0) ) )
        | ( ( ~ big_p(X3)
            | ~ big_p(esk1_1(X3)) )
          & ( big_p(X3)
            | big_p(esk1_1(X3)) ) ) ) ),
    inference(shift_quantors,[status(thm)],[5]) ).

fof(7,negated_conjecture,
    ! [X3,X5,X8,X10,X11,X12] :
      ( ( ~ big_p(esk4_0)
        | big_p(X10)
        | big_p(X12)
        | ~ big_p(X11) )
      & ( ~ big_p(X10)
        | big_p(esk4_0)
        | big_p(X12)
        | ~ big_p(X11) )
      & ( ~ big_p(esk4_0)
        | big_p(X10)
        | ~ big_p(esk5_0)
        | big_p(esk6_0) )
      & ( ~ big_p(X10)
        | big_p(esk4_0)
        | ~ big_p(esk5_0)
        | big_p(esk6_0) )
      & ( ~ big_p(X3)
        | ~ big_p(esk1_1(X3))
        | big_p(X8)
        | big_p(esk3_0) )
      & ( big_p(X3)
        | big_p(esk1_1(X3))
        | big_p(X8)
        | big_p(esk3_0) )
      & ( ~ big_p(X3)
        | ~ big_p(esk1_1(X3))
        | ~ big_p(X5)
        | ~ big_p(esk2_0) )
      & ( big_p(X3)
        | big_p(esk1_1(X3))
        | ~ big_p(X5)
        | ~ big_p(esk2_0) ) ),
    inference(distribute,[status(thm)],[6]) ).

cnf(9,negated_conjecture,
    ( ~ big_p(esk2_0)
    | ~ big_p(X1)
    | ~ big_p(esk1_1(X2))
    | ~ big_p(X2) ),
    inference(split_conjunct,[status(thm)],[7]) ).

cnf(10,negated_conjecture,
    ( big_p(esk3_0)
    | big_p(X1)
    | big_p(esk1_1(X2))
    | big_p(X2) ),
    inference(split_conjunct,[status(thm)],[7]) ).

cnf(14,negated_conjecture,
    ( big_p(X2)
    | big_p(esk4_0)
    | ~ big_p(X1)
    | ~ big_p(X3) ),
    inference(split_conjunct,[status(thm)],[7]) ).

cnf(15,negated_conjecture,
    ( big_p(X2)
    | big_p(X3)
    | ~ big_p(X1)
    | ~ big_p(esk4_0) ),
    inference(split_conjunct,[status(thm)],[7]) ).

cnf(16,negated_conjecture,
    ( big_p(esk3_0)
    | big_p(esk1_1(X3))
    | big_p(X3) ),
    inference(ef,[status(thm)],[10,theory(equality)]) ).

fof(24,plain,
    ( ~ epred1_0
  <=> ! [X2] :
        ( ~ big_p(X2)
        | ~ big_p(esk2_0)
        | ~ big_p(esk1_1(X2)) ) ),
    introduced(definition),
    [split] ).

cnf(25,plain,
    ( epred1_0
    | ~ big_p(X2)
    | ~ big_p(esk2_0)
    | ~ big_p(esk1_1(X2)) ),
    inference(split_equiv,[status(thm)],[24]) ).

fof(26,plain,
    ( ~ epred2_0
  <=> ! [X1] : ~ big_p(X1) ),
    introduced(definition),
    [split] ).

cnf(27,plain,
    ( epred2_0
    | ~ big_p(X1) ),
    inference(split_equiv,[status(thm)],[26]) ).

cnf(28,negated_conjecture,
    ( ~ epred2_0
    | ~ epred1_0 ),
    inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[9,24,theory(equality)]),26,theory(equality)]),
    [split] ).

cnf(29,negated_conjecture,
    ( big_p(esk4_0)
    | big_p(X1)
    | big_p(esk3_0)
    | big_p(X2)
    | ~ big_p(X3) ),
    inference(spm,[status(thm)],[14,16,theory(equality)]) ).

cnf(32,negated_conjecture,
    ( epred2_0
    | big_p(esk3_0)
    | big_p(X1) ),
    inference(spm,[status(thm)],[27,16,theory(equality)]) ).

cnf(33,negated_conjecture,
    ( epred2_0
    | big_p(esk3_0) ),
    inference(csr,[status(thm)],[32,27]) ).

cnf(34,negated_conjecture,
    epred2_0,
    inference(csr,[status(thm)],[33,27]) ).

cnf(36,negated_conjecture,
    ( $false
    | ~ epred1_0 ),
    inference(rw,[status(thm)],[28,34,theory(equality)]) ).

cnf(37,negated_conjecture,
    ~ epred1_0,
    inference(cn,[status(thm)],[36,theory(equality)]) ).

cnf(38,negated_conjecture,
    ( ~ big_p(X2)
    | ~ big_p(esk2_0)
    | ~ big_p(esk1_1(X2)) ),
    inference(sr,[status(thm)],[25,37,theory(equality)]) ).

cnf(42,negated_conjecture,
    ( big_p(esk4_0)
    | big_p(esk3_0)
    | big_p(X1)
    | ~ big_p(X3) ),
    inference(csr,[status(thm)],[29,14]) ).

cnf(43,negated_conjecture,
    ( big_p(esk4_0)
    | big_p(X1)
    | ~ big_p(X3) ),
    inference(csr,[status(thm)],[42,14]) ).

cnf(44,negated_conjecture,
    ( big_p(esk4_0)
    | big_p(X1)
    | big_p(esk3_0)
    | big_p(X2) ),
    inference(spm,[status(thm)],[43,16,theory(equality)]) ).

cnf(45,negated_conjecture,
    ( big_p(esk4_0)
    | big_p(esk3_0)
    | big_p(X1) ),
    inference(csr,[status(thm)],[44,43]) ).

cnf(46,negated_conjecture,
    ( big_p(esk4_0)
    | big_p(X1) ),
    inference(csr,[status(thm)],[45,43]) ).

cnf(47,negated_conjecture,
    big_p(esk4_0),
    inference(ef,[status(thm)],[46,theory(equality)]) ).

cnf(56,negated_conjecture,
    ( big_p(X1)
    | big_p(X2)
    | $false
    | ~ big_p(X3) ),
    inference(rw,[status(thm)],[15,47,theory(equality)]) ).

cnf(57,negated_conjecture,
    ( big_p(X1)
    | big_p(X2)
    | ~ big_p(X3) ),
    inference(cn,[status(thm)],[56,theory(equality)]) ).

cnf(58,negated_conjecture,
    ( big_p(X1)
    | big_p(X2) ),
    inference(spm,[status(thm)],[57,47,theory(equality)]) ).

cnf(62,negated_conjecture,
    ( big_p(X2)
    | ~ big_p(esk2_0)
    | ~ big_p(X1) ),
    inference(spm,[status(thm)],[38,58,theory(equality)]) ).

cnf(64,negated_conjecture,
    ( big_p(X2)
    | ~ big_p(esk2_0) ),
    inference(csr,[status(thm)],[62,58]) ).

cnf(65,negated_conjecture,
    big_p(X2),
    inference(csr,[status(thm)],[64,58]) ).

cnf(70,negated_conjecture,
    ( $false
    | ~ big_p(esk2_0)
    | ~ big_p(X1) ),
    inference(rw,[status(thm)],[38,65,theory(equality)]) ).

cnf(71,negated_conjecture,
    ( $false
    | $false
    | ~ big_p(X1) ),
    inference(rw,[status(thm)],[70,65,theory(equality)]) ).

cnf(72,negated_conjecture,
    ( $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[71,65,theory(equality)]) ).

cnf(73,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[72,theory(equality)]) ).

cnf(74,negated_conjecture,
    $false,
    73,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SYN/SYN374+1.p
% --creating new selector for []
% -running prover on /tmp/tmpJ3R9bm/sel_SYN374+1.p_1 with time limit 29
% -prover status Theorem
% Problem SYN374+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SYN/SYN374+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SYN/SYN374+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------