TSTP Solution File: SEU151+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU151+3 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 04:53:38 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   37 (  19 unt;   0 def)
%            Number of atoms       :  132 (  97 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  155 (  60   ~;  58   |;  35   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   67 (   4 sgn  36   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2,X3,X4] :
      ~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
        & X1 != X3
        & X1 != X4 ),
    file('/tmp/tmp4JfM-L/sel_SEU151+3.p_1',t10_zfmisc_1) ).

fof(3,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmp4JfM-L/sel_SEU151+3.p_1',commutativity_k2_tarski) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/tmp/tmp4JfM-L/sel_SEU151+3.p_1',d2_tarski) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
          & X1 != X3
          & X1 != X4 ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(13,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
      & X1 != X3
      & X1 != X4 ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(14,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( unordered_pair(X5,X6) = unordered_pair(X7,X8)
      & X5 != X7
      & X5 != X8 ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    ( unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk5_0)
    & esk2_0 != esk4_0
    & esk2_0 != esk5_0 ),
    inference(skolemize,[status(esa)],[14]) ).

cnf(16,negated_conjecture,
    esk2_0 != esk5_0,
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,negated_conjecture,
    esk2_0 != esk4_0,
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(18,negated_conjecture,
    unordered_pair(esk2_0,esk3_0) = unordered_pair(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(19,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(20,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(27,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(28,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)],[27]) ).

fof(29,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(esk7_3(X5,X6,X7),X7)
            | ( esk7_3(X5,X6,X7) != X5
              & esk7_3(X5,X6,X7) != X6 ) )
          & ( in(esk7_3(X5,X6,X7),X7)
            | esk7_3(X5,X6,X7) = X5
            | esk7_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(skolemize,[status(esa)],[28]) ).

fof(30,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(esk7_3(X5,X6,X7),X7)
            | ( esk7_3(X5,X6,X7) != X5
              & esk7_3(X5,X6,X7) != X6 ) )
          & ( in(esk7_3(X5,X6,X7),X7)
            | esk7_3(X5,X6,X7) = X5
            | esk7_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[29]) ).

fof(31,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) )
      & ( esk7_3(X5,X6,X7) != X5
        | ~ in(esk7_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( esk7_3(X5,X6,X7) != X6
        | ~ in(esk7_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( in(esk7_3(X5,X6,X7),X7)
        | esk7_3(X5,X6,X7) = X5
        | esk7_3(X5,X6,X7) = X6
        | X7 = unordered_pair(X5,X6) ) ),
    inference(distribute,[status(thm)],[30]) ).

cnf(35,plain,
    ( in(X4,X1)
    | X1 != unordered_pair(X2,X3)
    | X4 != X3 ),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(37,plain,
    ( X4 = X3
    | X4 = X2
    | X1 != unordered_pair(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(38,plain,
    ( in(X1,X2)
    | unordered_pair(X3,X1) != X2 ),
    inference(er,[status(thm)],[35,theory(equality)]) ).

cnf(40,plain,
    ( X1 = X2
    | X3 = X2
    | ~ in(X2,unordered_pair(X1,X3)) ),
    inference(er,[status(thm)],[37,theory(equality)]) ).

cnf(45,plain,
    in(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[38,theory(equality)]) ).

cnf(49,negated_conjecture,
    in(esk5_0,unordered_pair(esk2_0,esk3_0)),
    inference(spm,[status(thm)],[45,18,theory(equality)]) ).

cnf(50,plain,
    in(X1,unordered_pair(X1,X2)),
    inference(spm,[status(thm)],[45,20,theory(equality)]) ).

cnf(54,negated_conjecture,
    in(esk4_0,unordered_pair(esk2_0,esk3_0)),
    inference(spm,[status(thm)],[50,18,theory(equality)]) ).

cnf(78,negated_conjecture,
    ( esk3_0 = esk5_0
    | esk2_0 = esk5_0 ),
    inference(spm,[status(thm)],[40,49,theory(equality)]) ).

cnf(83,negated_conjecture,
    esk3_0 = esk5_0,
    inference(sr,[status(thm)],[78,16,theory(equality)]) ).

cnf(85,negated_conjecture,
    in(esk4_0,unordered_pair(esk2_0,esk5_0)),
    inference(rw,[status(thm)],[54,83,theory(equality)]) ).

cnf(87,negated_conjecture,
    unordered_pair(esk4_0,esk5_0) = unordered_pair(esk2_0,esk5_0),
    inference(rw,[status(thm)],[18,83,theory(equality)]) ).

cnf(101,negated_conjecture,
    ( esk5_0 = esk4_0
    | esk2_0 = esk4_0 ),
    inference(spm,[status(thm)],[40,85,theory(equality)]) ).

cnf(102,negated_conjecture,
    esk5_0 = esk4_0,
    inference(sr,[status(thm)],[101,17,theory(equality)]) ).

cnf(104,negated_conjecture,
    unordered_pair(esk4_0,esk4_0) = unordered_pair(esk2_0,esk5_0),
    inference(rw,[status(thm)],[87,102,theory(equality)]) ).

cnf(105,negated_conjecture,
    unordered_pair(esk4_0,esk4_0) = unordered_pair(esk2_0,esk4_0),
    inference(rw,[status(thm)],[104,102,theory(equality)]) ).

cnf(118,negated_conjecture,
    ( esk4_0 = X1
    | ~ in(X1,unordered_pair(esk2_0,esk4_0)) ),
    inference(spm,[status(thm)],[40,105,theory(equality)]) ).

cnf(127,negated_conjecture,
    esk4_0 = esk2_0,
    inference(spm,[status(thm)],[118,50,theory(equality)]) ).

cnf(129,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[127,17,theory(equality)]) ).

cnf(130,negated_conjecture,
    $false,
    129,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU151+3.p
% --creating new selector for []
% -running prover on /tmp/tmp4JfM-L/sel_SEU151+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU151+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU151+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU151+3.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
% 
%------------------------------------------------------------------------------