TSTP Solution File: SWC210+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC210+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 10:51:54 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   37 (  15 unt;   0 def)
%            Number of atoms       :  154 (  30 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  178 (  61   ~;  57   |;  45   &)
%                                         (   1 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   32 (   0 sgn  22   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpmAe67y/sel_SWC210+1.p_1',ax15) ).

fof(8,axiom,
    ssList(nil),
    file('/tmp/tmpmAe67y/sel_SWC210+1.p_1',ax17) ).

fof(9,axiom,
    ~ singletonP(nil),
    file('/tmp/tmpmAe67y/sel_SWC210+1.p_1',ax39) ).

fof(12,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ( ~ neq(X2,nil)
                        | ~ singletonP(X3)
                        | neq(X1,nil) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/tmp/tmpmAe67y/sel_SWC210+1.p_1',co1) ).

fof(13,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ~ singletonP(X3)
                          | neq(X1,nil) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[12]) ).

fof(14,plain,
    ~ singletonP(nil),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

fof(15,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ~ singletonP(X3)
                          | neq(X1,nil) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[13,theory(equality)]) ).

fof(46,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(47,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[47]) ).

fof(49,plain,
    ! [X3,X4] :
      ( ( ~ neq(X3,X4)
        | X3 != X4
        | ~ ssList(X4)
        | ~ ssList(X3) )
      & ( X3 = X4
        | neq(X3,X4)
        | ~ ssList(X4)
        | ~ ssList(X3) ) ),
    inference(distribute,[status(thm)],[48]) ).

cnf(50,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[49]) ).

cnf(56,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[8]) ).

cnf(57,plain,
    ~ singletonP(nil),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(68,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ( neq(X2,nil)
                      & singletonP(X3)
                      & ~ neq(X1,nil) )
                    | ( neq(X2,nil)
                      & ~ neq(X4,nil) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(69,negated_conjecture,
    ? [X5] :
      ( ssList(X5)
      & ? [X6] :
          ( ssList(X6)
          & ? [X7] :
              ( ssList(X7)
              & ? [X8] :
                  ( ssList(X8)
                  & X6 = X8
                  & X5 = X7
                  & ( ( neq(X6,nil)
                      & singletonP(X7)
                      & ~ neq(X5,nil) )
                    | ( neq(X6,nil)
                      & ~ neq(X8,nil) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[68]) ).

fof(70,negated_conjecture,
    ( ssList(esk6_0)
    & ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & esk7_0 = esk9_0
    & esk6_0 = esk8_0
    & ( ( neq(esk7_0,nil)
        & singletonP(esk8_0)
        & ~ neq(esk6_0,nil) )
      | ( neq(esk7_0,nil)
        & ~ neq(esk9_0,nil) ) ) ),
    inference(skolemize,[status(esa)],[69]) ).

fof(71,negated_conjecture,
    ( ssList(esk6_0)
    & ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & esk7_0 = esk9_0
    & esk6_0 = esk8_0
    & ( neq(esk7_0,nil)
      | neq(esk7_0,nil) )
    & ( ~ neq(esk9_0,nil)
      | neq(esk7_0,nil) )
    & ( neq(esk7_0,nil)
      | singletonP(esk8_0) )
    & ( ~ neq(esk9_0,nil)
      | singletonP(esk8_0) )
    & ( neq(esk7_0,nil)
      | ~ neq(esk6_0,nil) )
    & ( ~ neq(esk9_0,nil)
      | ~ neq(esk6_0,nil) ) ),
    inference(distribute,[status(thm)],[70]) ).

cnf(72,negated_conjecture,
    ( ~ neq(esk6_0,nil)
    | ~ neq(esk9_0,nil) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(74,negated_conjecture,
    ( singletonP(esk8_0)
    | ~ neq(esk9_0,nil) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(77,negated_conjecture,
    ( neq(esk7_0,nil)
    | neq(esk7_0,nil) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(78,negated_conjecture,
    esk6_0 = esk8_0,
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(79,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(83,negated_conjecture,
    ssList(esk6_0),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(90,negated_conjecture,
    ( singletonP(esk6_0)
    | ~ neq(esk9_0,nil) ),
    inference(rw,[status(thm)],[74,78,theory(equality)]) ).

cnf(91,negated_conjecture,
    ( singletonP(esk6_0)
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[90,79,theory(equality)]),77,theory(equality)]) ).

cnf(92,negated_conjecture,
    singletonP(esk6_0),
    inference(cn,[status(thm)],[91,theory(equality)]) ).

cnf(97,negated_conjecture,
    ( ~ neq(esk6_0,nil)
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[72,79,theory(equality)]),77,theory(equality)]) ).

cnf(98,negated_conjecture,
    ~ neq(esk6_0,nil),
    inference(cn,[status(thm)],[97,theory(equality)]) ).

cnf(99,negated_conjecture,
    ( esk6_0 = nil
    | ~ ssList(nil)
    | ~ ssList(esk6_0) ),
    inference(spm,[status(thm)],[98,50,theory(equality)]) ).

cnf(100,negated_conjecture,
    ( esk6_0 = nil
    | $false
    | ~ ssList(esk6_0) ),
    inference(rw,[status(thm)],[99,56,theory(equality)]) ).

cnf(101,negated_conjecture,
    ( esk6_0 = nil
    | $false
    | $false ),
    inference(rw,[status(thm)],[100,83,theory(equality)]) ).

cnf(102,negated_conjecture,
    esk6_0 = nil,
    inference(cn,[status(thm)],[101,theory(equality)]) ).

cnf(139,negated_conjecture,
    singletonP(nil),
    inference(rw,[status(thm)],[92,102,theory(equality)]) ).

cnf(145,plain,
    $false,
    inference(rw,[status(thm)],[57,139,theory(equality)]) ).

cnf(146,plain,
    $false,
    inference(cn,[status(thm)],[145,theory(equality)]) ).

cnf(147,plain,
    $false,
    146,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC210+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpmAe67y/sel_SWC210+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC210+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC210+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC210+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
% 
%------------------------------------------------------------------------------