TSTP Solution File: SEU159+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU159+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 04:56:03 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   49 (  10 unt;   0 def)
%            Number of atoms       :  209 (  71 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  252 (  92   ~; 109   |;  45   &)
%                                         (   5 <=>;   1  =>;   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    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :  100 (   4 sgn  52   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2,X3] :
      ( subset(unordered_pair(X1,X2),X3)
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',t38_zfmisc_1) ).

fof(3,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',commutativity_k2_tarski) ).

fof(5,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',d3_tarski) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/tmp/tmpx-FJec/sel_SEU159+1.p_1',d2_tarski) ).

fof(8,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(unordered_pair(X1,X2),X3)
      <=> ( in(X1,X3)
          & in(X2,X3) ) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(11,negated_conjecture,
    ? [X1,X2,X3] :
      ( ( ~ subset(unordered_pair(X1,X2),X3)
        | ~ in(X1,X3)
        | ~ in(X2,X3) )
      & ( subset(unordered_pair(X1,X2),X3)
        | ( in(X1,X3)
          & in(X2,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(12,negated_conjecture,
    ? [X4,X5,X6] :
      ( ( ~ subset(unordered_pair(X4,X5),X6)
        | ~ in(X4,X6)
        | ~ in(X5,X6) )
      & ( subset(unordered_pair(X4,X5),X6)
        | ( in(X4,X6)
          & in(X5,X6) ) ) ),
    inference(variable_rename,[status(thm)],[11]) ).

fof(13,negated_conjecture,
    ( ( ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0)
      | ~ in(esk1_0,esk3_0)
      | ~ in(esk2_0,esk3_0) )
    & ( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
      | ( in(esk1_0,esk3_0)
        & in(esk2_0,esk3_0) ) ) ),
    inference(skolemize,[status(esa)],[12]) ).

fof(14,negated_conjecture,
    ( ( ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0)
      | ~ in(esk1_0,esk3_0)
      | ~ in(esk2_0,esk3_0) )
    & ( in(esk1_0,esk3_0)
      | subset(unordered_pair(esk1_0,esk2_0),esk3_0) )
    & ( in(esk2_0,esk3_0)
      | subset(unordered_pair(esk1_0,esk2_0),esk3_0) ) ),
    inference(distribute,[status(thm)],[13]) ).

cnf(15,negated_conjecture,
    ( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
    | in(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(16,negated_conjecture,
    ( subset(unordered_pair(esk1_0,esk2_0),esk3_0)
    | in(esk1_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(17,negated_conjecture,
    ( ~ in(esk2_0,esk3_0)
    | ~ in(esk1_0,esk3_0)
    | ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(18,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(19,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(23,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X2) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(24,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ? [X7] :
            ( in(X7,X4)
            & ~ in(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[23]) ).

fof(25,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ( in(esk4_2(X4,X5),X4)
          & ~ in(esk4_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[24]) ).

fof(26,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( in(esk4_2(X4,X5),X4)
          & ~ in(esk4_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[25]) ).

fof(27,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( in(esk4_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk4_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[26]) ).

cnf(28,plain,
    ( subset(X1,X2)
    | ~ in(esk4_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(29,plain,
    ( subset(X1,X2)
    | in(esk4_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(30,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(31,plain,
    ! [X1,X2,X3] :
      ( ( X3 != unordered_pair(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | X4 = X1
              | X4 = X2 )
            & ( ( X4 != X1
                & X4 != X2 )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ( X4 != X1
                & X4 != X2 ) )
            & ( in(X4,X3)
              | X4 = X1
              | X4 = X2 ) )
        | X3 = unordered_pair(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(32,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ( X9 != X5
                & X9 != X6 ) )
            & ( in(X9,X7)
              | X9 = X5
              | X9 = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[31]) ).

fof(33,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
            | ( esk5_3(X5,X6,X7) != X5
              & esk5_3(X5,X6,X7) != X6 ) )
          & ( in(esk5_3(X5,X6,X7),X7)
            | esk5_3(X5,X6,X7) = X5
            | esk5_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(skolemize,[status(esa)],[32]) ).

fof(34,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | X8 = X5
            | X8 = X6 )
          & ( ( X8 != X5
              & X8 != X6 )
            | in(X8,X7) ) )
        | X7 != unordered_pair(X5,X6) )
      & ( ( ( ~ in(esk5_3(X5,X6,X7),X7)
            | ( esk5_3(X5,X6,X7) != X5
              & esk5_3(X5,X6,X7) != X6 ) )
          & ( in(esk5_3(X5,X6,X7),X7)
            | esk5_3(X5,X6,X7) = X5
            | esk5_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[33]) ).

fof(35,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,X7)
        | X8 = X5
        | X8 = X6
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X5
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X6
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( esk5_3(X5,X6,X7) != X5
        | ~ in(esk5_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( esk5_3(X5,X6,X7) != X6
        | ~ in(esk5_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( in(esk5_3(X5,X6,X7),X7)
        | esk5_3(X5,X6,X7) = X5
        | esk5_3(X5,X6,X7) = X6
        | X7 = unordered_pair(X5,X6) ) ),
    inference(distribute,[status(thm)],[34]) ).

cnf(39,plain,
    ( in(X4,X1)
    | X1 != unordered_pair(X2,X3)
    | X4 != X3 ),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(41,plain,
    ( X4 = X3
    | X4 = X2
    | X1 != unordered_pair(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(45,negated_conjecture,
    ( in(X1,esk3_0)
    | in(esk1_0,esk3_0)
    | ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[30,16,theory(equality)]) ).

cnf(46,negated_conjecture,
    ( in(X1,esk3_0)
    | in(esk2_0,esk3_0)
    | ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[30,15,theory(equality)]) ).

cnf(50,plain,
    ( in(X1,X2)
    | unordered_pair(X3,X1) != X2 ),
    inference(er,[status(thm)],[39,theory(equality)]) ).

cnf(54,plain,
    ( X1 = X2
    | X3 = X2
    | ~ in(X2,unordered_pair(X1,X3)) ),
    inference(er,[status(thm)],[41,theory(equality)]) ).

cnf(64,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[50,theory(equality)]) ).

cnf(67,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(spm,[status(thm)],[64,19,theory(equality)]) ).

cnf(71,negated_conjecture,
    in(esk2_0,esk3_0),
    inference(spm,[status(thm)],[46,64,theory(equality)]) ).

cnf(76,negated_conjecture,
    ( ~ in(esk1_0,esk3_0)
    | $false
    | ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
    inference(rw,[status(thm)],[17,71,theory(equality)]) ).

cnf(77,negated_conjecture,
    ( ~ in(esk1_0,esk3_0)
    | ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
    inference(cn,[status(thm)],[76,theory(equality)]) ).

cnf(83,negated_conjecture,
    in(esk1_0,esk3_0),
    inference(spm,[status(thm)],[45,67,theory(equality)]) ).

cnf(94,negated_conjecture,
    ( $false
    | ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0) ),
    inference(rw,[status(thm)],[77,83,theory(equality)]) ).

cnf(95,negated_conjecture,
    ~ subset(unordered_pair(esk1_0,esk2_0),esk3_0),
    inference(cn,[status(thm)],[94,theory(equality)]) ).

cnf(101,plain,
    ( X1 = esk4_2(unordered_pair(X2,X1),X3)
    | X2 = esk4_2(unordered_pair(X2,X1),X3)
    | subset(unordered_pair(X2,X1),X3) ),
    inference(spm,[status(thm)],[54,29,theory(equality)]) ).

cnf(109,plain,
    ( subset(unordered_pair(X1,X2),X3)
    | esk4_2(unordered_pair(X1,X2),X3) = X2
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[28,101,theory(equality)]) ).

cnf(189,plain,
    ( subset(unordered_pair(X1,X2),X3)
    | ~ in(X2,X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[28,109,theory(equality)]) ).

cnf(194,negated_conjecture,
    ( ~ in(esk2_0,esk3_0)
    | ~ in(esk1_0,esk3_0) ),
    inference(spm,[status(thm)],[95,189,theory(equality)]) ).

cnf(196,negated_conjecture,
    ( $false
    | ~ in(esk1_0,esk3_0) ),
    inference(rw,[status(thm)],[194,71,theory(equality)]) ).

cnf(197,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[196,83,theory(equality)]) ).

cnf(198,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[197,theory(equality)]) ).

cnf(199,negated_conjecture,
    $false,
    198,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU159+1.p
% --creating new selector for []
% -running prover on /tmp/tmpx-FJec/sel_SEU159+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU159+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU159+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU159+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
% 
%------------------------------------------------------------------------------