TSTP Solution File: NUM386+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM386+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n106.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan  8 15:21:14 EST 2018

% Result   : Theorem 0.07s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   48 (   8 unt;   0 def)
%            Number of atoms       :  229 (  21 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  286 ( 105   ~; 127   |;  48   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   88 (   4 sgn  48   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(17,conjecture,
    ! [X1,X2] :
      ( in(X1,succ(X2))
    <=> ( in(X1,X2)
        | equal(X1,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmpBNZy0P/sel_theBenchmark.p_1',t13_ordinal1) ).

fof(18,axiom,
    ! [X1] : equal(succ(X1),set_union2(X1,singleton(X1))),
    file('/export/starexec/sandbox2/tmp/tmpBNZy0P/sel_theBenchmark.p_1',d1_ordinal1) ).

fof(20,axiom,
    ! [X1,X2,X3] :
      ( equal(X3,set_union2(X1,X2))
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmpBNZy0P/sel_theBenchmark.p_1',d2_xboole_0) ).

fof(30,axiom,
    ! [X1,X2] :
      ( equal(X2,singleton(X1))
    <=> ! [X3] :
          ( in(X3,X2)
        <=> equal(X3,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmpBNZy0P/sel_theBenchmark.p_1',d1_tarski) ).

fof(35,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X1,succ(X2))
      <=> ( in(X1,X2)
          | equal(X1,X2) ) ),
    inference(assume_negation,[status(cth)],[17]) ).

fof(95,negated_conjecture,
    ? [X1,X2] :
      ( ( ~ in(X1,succ(X2))
        | ( ~ in(X1,X2)
          & ~ equal(X1,X2) ) )
      & ( in(X1,succ(X2))
        | in(X1,X2)
        | equal(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(96,negated_conjecture,
    ? [X3,X4] :
      ( ( ~ in(X3,succ(X4))
        | ( ~ in(X3,X4)
          & ~ equal(X3,X4) ) )
      & ( in(X3,succ(X4))
        | in(X3,X4)
        | equal(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[95]) ).

fof(97,negated_conjecture,
    ( ( ~ in(esk6_0,succ(esk7_0))
      | ( ~ in(esk6_0,esk7_0)
        & ~ equal(esk6_0,esk7_0) ) )
    & ( in(esk6_0,succ(esk7_0))
      | in(esk6_0,esk7_0)
      | equal(esk6_0,esk7_0) ) ),
    inference(skolemize,[status(esa)],[96]) ).

fof(98,negated_conjecture,
    ( ( ~ in(esk6_0,esk7_0)
      | ~ in(esk6_0,succ(esk7_0)) )
    & ( ~ equal(esk6_0,esk7_0)
      | ~ in(esk6_0,succ(esk7_0)) )
    & ( in(esk6_0,succ(esk7_0))
      | in(esk6_0,esk7_0)
      | equal(esk6_0,esk7_0) ) ),
    inference(distribute,[status(thm)],[97]) ).

cnf(99,negated_conjecture,
    ( esk6_0 = esk7_0
    | in(esk6_0,esk7_0)
    | in(esk6_0,succ(esk7_0)) ),
    inference(split_conjunct,[status(thm)],[98]) ).

cnf(100,negated_conjecture,
    ( ~ in(esk6_0,succ(esk7_0))
    | esk6_0 != esk7_0 ),
    inference(split_conjunct,[status(thm)],[98]) ).

cnf(101,negated_conjecture,
    ( ~ in(esk6_0,succ(esk7_0))
    | ~ in(esk6_0,esk7_0) ),
    inference(split_conjunct,[status(thm)],[98]) ).

fof(102,plain,
    ! [X2] : equal(succ(X2),set_union2(X2,singleton(X2))),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(103,plain,
    succ(X1) = set_union2(X1,singleton(X1)),
    inference(split_conjunct,[status(thm)],[102]) ).

fof(106,plain,
    ! [X1,X2,X3] :
      ( ( ~ equal(X3,set_union2(X1,X2))
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | in(X4,X1)
              | in(X4,X2) )
            & ( ( ~ in(X4,X1)
                & ~ in(X4,X2) )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) )
            & ( in(X4,X3)
              | in(X4,X1)
              | in(X4,X2) ) )
        | equal(X3,set_union2(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(107,plain,
    ! [X5,X6,X7] :
      ( ( ~ equal(X7,set_union2(X5,X6))
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | in(X8,X5)
              | in(X8,X6) )
            & ( ( ~ in(X8,X5)
                & ~ in(X8,X6) )
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ( ~ in(X9,X5)
                & ~ in(X9,X6) ) )
            & ( in(X9,X7)
              | in(X9,X5)
              | in(X9,X6) ) )
        | equal(X7,set_union2(X5,X6)) ) ),
    inference(variable_rename,[status(thm)],[106]) ).

fof(108,plain,
    ! [X5,X6,X7] :
      ( ( ~ equal(X7,set_union2(X5,X6))
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | in(X8,X5)
              | in(X8,X6) )
            & ( ( ~ in(X8,X5)
                & ~ in(X8,X6) )
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
            | ( ~ in(esk8_3(X5,X6,X7),X5)
              & ~ in(esk8_3(X5,X6,X7),X6) ) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | in(esk8_3(X5,X6,X7),X5)
            | in(esk8_3(X5,X6,X7),X6) ) )
        | equal(X7,set_union2(X5,X6)) ) ),
    inference(skolemize,[status(esa)],[107]) ).

fof(109,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | in(X8,X5)
            | in(X8,X6) )
          & ( ( ~ in(X8,X5)
              & ~ in(X8,X6) )
            | in(X8,X7) ) )
        | ~ equal(X7,set_union2(X5,X6)) )
      & ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
            | ( ~ in(esk8_3(X5,X6,X7),X5)
              & ~ in(esk8_3(X5,X6,X7),X6) ) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | in(esk8_3(X5,X6,X7),X5)
            | in(esk8_3(X5,X6,X7),X6) ) )
        | equal(X7,set_union2(X5,X6)) ) ),
    inference(shift_quantors,[status(thm)],[108]) ).

fof(110,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,X7)
        | in(X8,X5)
        | in(X8,X6)
        | ~ equal(X7,set_union2(X5,X6)) )
      & ( ~ in(X8,X5)
        | in(X8,X7)
        | ~ equal(X7,set_union2(X5,X6)) )
      & ( ~ in(X8,X6)
        | in(X8,X7)
        | ~ equal(X7,set_union2(X5,X6)) )
      & ( ~ in(esk8_3(X5,X6,X7),X5)
        | ~ in(esk8_3(X5,X6,X7),X7)
        | equal(X7,set_union2(X5,X6)) )
      & ( ~ in(esk8_3(X5,X6,X7),X6)
        | ~ in(esk8_3(X5,X6,X7),X7)
        | equal(X7,set_union2(X5,X6)) )
      & ( in(esk8_3(X5,X6,X7),X7)
        | in(esk8_3(X5,X6,X7),X5)
        | in(esk8_3(X5,X6,X7),X6)
        | equal(X7,set_union2(X5,X6)) ) ),
    inference(distribute,[status(thm)],[109]) ).

cnf(114,plain,
    ( in(X4,X1)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[110]) ).

cnf(115,plain,
    ( in(X4,X1)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[110]) ).

cnf(116,plain,
    ( in(X4,X3)
    | in(X4,X2)
    | X1 != set_union2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[110]) ).

fof(142,plain,
    ! [X1,X2] :
      ( ( ~ equal(X2,singleton(X1))
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | equal(X3,X1) )
            & ( ~ equal(X3,X1)
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ equal(X3,X1) )
            & ( in(X3,X2)
              | equal(X3,X1) ) )
        | equal(X2,singleton(X1)) ) ),
    inference(fof_nnf,[status(thm)],[30]) ).

fof(143,plain,
    ! [X4,X5] :
      ( ( ~ equal(X5,singleton(X4))
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | equal(X6,X4) )
            & ( ~ equal(X6,X4)
              | in(X6,X5) ) ) )
      & ( ? [X7] :
            ( ( ~ in(X7,X5)
              | ~ equal(X7,X4) )
            & ( in(X7,X5)
              | equal(X7,X4) ) )
        | equal(X5,singleton(X4)) ) ),
    inference(variable_rename,[status(thm)],[142]) ).

fof(144,plain,
    ! [X4,X5] :
      ( ( ~ equal(X5,singleton(X4))
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | equal(X6,X4) )
            & ( ~ equal(X6,X4)
              | in(X6,X5) ) ) )
      & ( ( ( ~ in(esk11_2(X4,X5),X5)
            | ~ equal(esk11_2(X4,X5),X4) )
          & ( in(esk11_2(X4,X5),X5)
            | equal(esk11_2(X4,X5),X4) ) )
        | equal(X5,singleton(X4)) ) ),
    inference(skolemize,[status(esa)],[143]) ).

fof(145,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ in(X6,X5)
            | equal(X6,X4) )
          & ( ~ equal(X6,X4)
            | in(X6,X5) ) )
        | ~ equal(X5,singleton(X4)) )
      & ( ( ( ~ in(esk11_2(X4,X5),X5)
            | ~ equal(esk11_2(X4,X5),X4) )
          & ( in(esk11_2(X4,X5),X5)
            | equal(esk11_2(X4,X5),X4) ) )
        | equal(X5,singleton(X4)) ) ),
    inference(shift_quantors,[status(thm)],[144]) ).

fof(146,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X5)
        | equal(X6,X4)
        | ~ equal(X5,singleton(X4)) )
      & ( ~ equal(X6,X4)
        | in(X6,X5)
        | ~ equal(X5,singleton(X4)) )
      & ( ~ in(esk11_2(X4,X5),X5)
        | ~ equal(esk11_2(X4,X5),X4)
        | equal(X5,singleton(X4)) )
      & ( in(esk11_2(X4,X5),X5)
        | equal(esk11_2(X4,X5),X4)
        | equal(X5,singleton(X4)) ) ),
    inference(distribute,[status(thm)],[145]) ).

cnf(149,plain,
    ( in(X3,X1)
    | X1 != singleton(X2)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[146]) ).

cnf(150,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[146]) ).

cnf(169,negated_conjecture,
    ( esk7_0 = esk6_0
    | in(esk6_0,esk7_0)
    | in(esk6_0,set_union2(esk7_0,singleton(esk7_0))) ),
    inference(rw,[status(thm)],[99,103,theory(equality)]),
    [unfolding] ).

cnf(171,negated_conjecture,
    ( esk7_0 != esk6_0
    | ~ in(esk6_0,set_union2(esk7_0,singleton(esk7_0))) ),
    inference(rw,[status(thm)],[100,103,theory(equality)]),
    [unfolding] ).

cnf(172,negated_conjecture,
    ( ~ in(esk6_0,esk7_0)
    | ~ in(esk6_0,set_union2(esk7_0,singleton(esk7_0))) ),
    inference(rw,[status(thm)],[101,103,theory(equality)]),
    [unfolding] ).

cnf(187,plain,
    ( in(X1,X2)
    | singleton(X1) != X2 ),
    inference(er,[status(thm)],[149,theory(equality)]) ).

cnf(204,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[114,theory(equality)]) ).

cnf(211,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[115,theory(equality)]) ).

cnf(220,plain,
    ( in(X1,X2)
    | in(X1,X3)
    | ~ in(X1,set_union2(X2,X3)) ),
    inference(er,[status(thm)],[116,theory(equality)]) ).

cnf(295,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[187,theory(equality)]) ).

cnf(344,negated_conjecture,
    ( esk6_0 != esk7_0
    | ~ in(esk6_0,singleton(esk7_0)) ),
    inference(spm,[status(thm)],[171,204,theory(equality)]) ).

cnf(366,negated_conjecture,
    ~ in(esk6_0,esk7_0),
    inference(spm,[status(thm)],[172,211,theory(equality)]) ).

cnf(370,negated_conjecture,
    ( esk6_0 = esk7_0
    | in(esk6_0,set_union2(esk7_0,singleton(esk7_0))) ),
    inference(sr,[status(thm)],[169,366,theory(equality)]) ).

cnf(398,negated_conjecture,
    ( in(esk6_0,singleton(esk7_0))
    | in(esk6_0,esk7_0)
    | esk6_0 = esk7_0 ),
    inference(spm,[status(thm)],[220,370,theory(equality)]) ).

cnf(399,negated_conjecture,
    ( in(esk6_0,singleton(esk7_0))
    | esk6_0 = esk7_0 ),
    inference(sr,[status(thm)],[398,366,theory(equality)]) ).

cnf(402,negated_conjecture,
    ( X1 = esk6_0
    | esk6_0 = esk7_0
    | singleton(X1) != singleton(esk7_0) ),
    inference(spm,[status(thm)],[150,399,theory(equality)]) ).

cnf(413,negated_conjecture,
    esk6_0 = esk7_0,
    inference(er,[status(thm)],[402,theory(equality)]) ).

cnf(430,negated_conjecture,
    ( $false
    | ~ in(esk6_0,singleton(esk7_0)) ),
    inference(rw,[status(thm)],[344,413,theory(equality)]) ).

cnf(431,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[430,413,theory(equality)]),295,theory(equality)]) ).

cnf(432,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[431,theory(equality)]) ).

cnf(433,negated_conjecture,
    $false,
    432,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM386+1 : TPTP v7.0.0. Released v3.2.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.24  % Computer : n106.star.cs.uiowa.edu
% 0.02/0.24  % Model    : x86_64 x86_64
% 0.02/0.24  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24  % Memory   : 32218.625MB
% 0.02/0.24  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24  % CPULimit : 300
% 0.02/0.24  % DateTime : Fri Jan  5 02:35:30 CST 2018
% 0.02/0.24  % CPUTime  : 
% 0.02/0.28  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.28  --creating new selector for []
% 0.07/0.37  -running prover on /export/starexec/sandbox2/tmp/tmpBNZy0P/sel_theBenchmark.p_1 with time limit 29
% 0.07/0.37  -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpBNZy0P/sel_theBenchmark.p_1']
% 0.07/0.37  -prover status Theorem
% 0.07/0.37  Problem theBenchmark.p solved in phase 0.
% 0.07/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37  Solved 1 out of 1.
% 0.07/0.37  # Problem is unsatisfiable (or provable), constructing proof object
% 0.07/0.37  # SZS status Theorem
% 0.07/0.37  # SZS output start CNFRefutation.
% See solution above
% 0.07/0.37  # SZS output end CNFRefutation
%------------------------------------------------------------------------------