TSTP Solution File: SWC013+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC013+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 10:05:22 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   61 (  11 unt;   0 def)
%            Number of atoms       :  386 ( 143 equ)
%            Maximal formula atoms :   38 (   6 avg)
%            Number of connectives :  548 ( 223   ~; 222   |;  84   &)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  113 (   0 sgn  53   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax22) ).

fof(18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax15) ).

fof(19,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax16) ).

fof(20,axiom,
    ssList(nil),
    file('/tmp/tmpah920q/sel_SWC013+1.p_1',ax17) ).

fof(23,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ( ~ neq(X2,nil)
                        | ? [X5] :
                            ( ssList(X5)
                            & X3 != X5
                            & ? [X6] :
                                ( ssItem(X6)
                                & cons(X6,nil) = X5
                                & hd(X4) = X6
                                & neq(nil,X4) ) )
                        | ? [X7] :
                            ( ssList(X7)
                            & X1 = X7
                            & ? [X8] :
                                ( ssItem(X8)
                                & cons(X8,nil) = X7
                                & hd(X2) = X8
                                & neq(nil,X2) ) ) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/tmp/tmpah920q/sel_SWC013+1.p_1',co1) ).

fof(24,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X3 != X5
                              & ? [X6] :
                                  ( ssItem(X6)
                                  & cons(X6,nil) = X5
                                  & hd(X4) = X6
                                  & neq(nil,X4) ) )
                          | ? [X7] :
                              ( ssList(X7)
                              & X1 = X7
                              & ? [X8] :
                                  ( ssItem(X8)
                                  & cons(X8,nil) = X7
                                  & hd(X2) = X8
                                  & neq(nil,X2) ) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[23]) ).

fof(25,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X3 != X5
                              & ? [X6] :
                                  ( ssItem(X6)
                                  & cons(X6,nil) = X5
                                  & hd(X4) = X6
                                  & neq(nil,X4) ) )
                          | ? [X7] :
                              ( ssList(X7)
                              & X1 = X7
                              & ? [X8] :
                                  ( ssItem(X8)
                                  & cons(X8,nil) = X7
                                  & hd(X2) = X8
                                  & neq(nil,X2) ) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).

fof(78,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ssItem(hd(X1)) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(79,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | nil = X2
      | ssItem(hd(X2)) ),
    inference(variable_rename,[status(thm)],[78]) ).

cnf(80,plain,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[79]) ).

fof(102,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(103,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[102]) ).

fof(104,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[103]) ).

fof(105,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)],[104]) ).

cnf(106,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(107,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | X1 != X2
    | ~ neq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[105]) ).

fof(108,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(109,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[108]) ).

fof(110,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[109]) ).

cnf(111,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[110]) ).

cnf(112,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(123,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ( neq(X2,nil)
                      & ! [X5] :
                          ( ~ ssList(X5)
                          | X3 = X5
                          | ! [X6] :
                              ( ~ ssItem(X6)
                              | cons(X6,nil) != X5
                              | hd(X4) != X6
                              | ~ neq(nil,X4) ) )
                      & ! [X7] :
                          ( ~ ssList(X7)
                          | X1 != X7
                          | ! [X8] :
                              ( ~ ssItem(X8)
                              | cons(X8,nil) != X7
                              | hd(X2) != X8
                              | ~ neq(nil,X2) ) ) )
                    | ( neq(X2,nil)
                      & ~ neq(X4,nil) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(124,negated_conjecture,
    ? [X9] :
      ( ssList(X9)
      & ? [X10] :
          ( ssList(X10)
          & ? [X11] :
              ( ssList(X11)
              & ? [X12] :
                  ( ssList(X12)
                  & X10 = X12
                  & X9 = X11
                  & ( ( neq(X10,nil)
                      & ! [X13] :
                          ( ~ ssList(X13)
                          | X11 = X13
                          | ! [X14] :
                              ( ~ ssItem(X14)
                              | cons(X14,nil) != X13
                              | hd(X12) != X14
                              | ~ neq(nil,X12) ) )
                      & ! [X15] :
                          ( ~ ssList(X15)
                          | X9 != X15
                          | ! [X16] :
                              ( ~ ssItem(X16)
                              | cons(X16,nil) != X15
                              | hd(X10) != X16
                              | ~ neq(nil,X10) ) ) )
                    | ( neq(X10,nil)
                      & ~ neq(X12,nil) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[123]) ).

fof(125,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)
        & ! [X13] :
            ( ~ ssList(X13)
            | esk8_0 = X13
            | ! [X14] :
                ( ~ ssItem(X14)
                | cons(X14,nil) != X13
                | hd(esk9_0) != X14
                | ~ neq(nil,esk9_0) ) )
        & ! [X15] :
            ( ~ ssList(X15)
            | esk6_0 != X15
            | ! [X16] :
                ( ~ ssItem(X16)
                | cons(X16,nil) != X15
                | hd(esk7_0) != X16
                | ~ neq(nil,esk7_0) ) ) )
      | ( neq(esk7_0,nil)
        & ~ neq(esk9_0,nil) ) ) ),
    inference(skolemize,[status(esa)],[124]) ).

fof(126,negated_conjecture,
    ! [X13,X14,X15,X16] :
      ( ( ( ( ~ ssItem(X16)
            | cons(X16,nil) != X15
            | hd(esk7_0) != X16
            | ~ neq(nil,esk7_0)
            | ~ ssList(X15)
            | esk6_0 != X15 )
          & ( ~ ssItem(X14)
            | cons(X14,nil) != X13
            | hd(esk9_0) != X14
            | ~ neq(nil,esk9_0)
            | ~ ssList(X13)
            | esk8_0 = X13 )
          & neq(esk7_0,nil) )
        | ( neq(esk7_0,nil)
          & ~ neq(esk9_0,nil) ) )
      & esk7_0 = esk9_0
      & esk6_0 = esk8_0
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0)
      & ssList(esk6_0) ),
    inference(shift_quantors,[status(thm)],[125]) ).

fof(127,negated_conjecture,
    ! [X13,X14,X15,X16] :
      ( ( neq(esk7_0,nil)
        | ~ ssItem(X16)
        | cons(X16,nil) != X15
        | hd(esk7_0) != X16
        | ~ neq(nil,esk7_0)
        | ~ ssList(X15)
        | esk6_0 != X15 )
      & ( ~ neq(esk9_0,nil)
        | ~ ssItem(X16)
        | cons(X16,nil) != X15
        | hd(esk7_0) != X16
        | ~ neq(nil,esk7_0)
        | ~ ssList(X15)
        | esk6_0 != X15 )
      & ( neq(esk7_0,nil)
        | ~ ssItem(X14)
        | cons(X14,nil) != X13
        | hd(esk9_0) != X14
        | ~ neq(nil,esk9_0)
        | ~ ssList(X13)
        | esk8_0 = X13 )
      & ( ~ neq(esk9_0,nil)
        | ~ ssItem(X14)
        | cons(X14,nil) != X13
        | hd(esk9_0) != X14
        | ~ neq(nil,esk9_0)
        | ~ ssList(X13)
        | esk8_0 = X13 )
      & ( neq(esk7_0,nil)
        | neq(esk7_0,nil) )
      & ( ~ neq(esk9_0,nil)
        | neq(esk7_0,nil) )
      & esk7_0 = esk9_0
      & esk6_0 = esk8_0
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0)
      & ssList(esk6_0) ),
    inference(distribute,[status(thm)],[126]) ).

cnf(129,negated_conjecture,
    ssList(esk7_0),
    inference(split_conjunct,[status(thm)],[127]) ).

cnf(132,negated_conjecture,
    esk6_0 = esk8_0,
    inference(split_conjunct,[status(thm)],[127]) ).

cnf(133,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[127]) ).

cnf(135,negated_conjecture,
    ( neq(esk7_0,nil)
    | neq(esk7_0,nil) ),
    inference(split_conjunct,[status(thm)],[127]) ).

cnf(136,negated_conjecture,
    ( esk8_0 = X1
    | ~ ssList(X1)
    | ~ neq(nil,esk9_0)
    | hd(esk9_0) != X2
    | cons(X2,nil) != X1
    | ~ ssItem(X2)
    | ~ neq(esk9_0,nil) ),
    inference(split_conjunct,[status(thm)],[127]) ).

cnf(138,negated_conjecture,
    ( esk6_0 != X1
    | ~ ssList(X1)
    | ~ neq(nil,esk7_0)
    | hd(esk7_0) != X2
    | cons(X2,nil) != X1
    | ~ ssItem(X2)
    | ~ neq(esk9_0,nil) ),
    inference(split_conjunct,[status(thm)],[127]) ).

cnf(158,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[107,theory(equality)]) ).

cnf(231,negated_conjecture,
    ( esk6_0 = X1
    | hd(esk9_0) != X2
    | cons(X2,nil) != X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ neq(nil,esk9_0)
    | ~ neq(esk9_0,nil) ),
    inference(rw,[status(thm)],[136,132,theory(equality)]) ).

cnf(232,negated_conjecture,
    ( esk6_0 = X1
    | hd(esk7_0) != X2
    | cons(X2,nil) != X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ neq(nil,esk9_0)
    | ~ neq(esk9_0,nil) ),
    inference(rw,[status(thm)],[231,133,theory(equality)]) ).

cnf(233,negated_conjecture,
    ( esk6_0 = X1
    | hd(esk7_0) != X2
    | cons(X2,nil) != X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ neq(nil,esk7_0)
    | ~ neq(esk9_0,nil) ),
    inference(rw,[status(thm)],[232,133,theory(equality)]) ).

cnf(234,negated_conjecture,
    ( esk6_0 = X1
    | hd(esk7_0) != X2
    | cons(X2,nil) != X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ neq(nil,esk7_0)
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[233,133,theory(equality)]),135,theory(equality)]) ).

cnf(235,negated_conjecture,
    ( esk6_0 = X1
    | hd(esk7_0) != X2
    | cons(X2,nil) != X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ neq(nil,esk7_0) ),
    inference(cn,[status(thm)],[234,theory(equality)]) ).

cnf(262,negated_conjecture,
    ( esk6_0 != X1
    | hd(esk7_0) != X2
    | cons(X2,nil) != X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ neq(nil,esk7_0)
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[138,133,theory(equality)]),135,theory(equality)]) ).

cnf(263,negated_conjecture,
    ( esk6_0 != X1
    | hd(esk7_0) != X2
    | cons(X2,nil) != X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ neq(nil,esk7_0) ),
    inference(cn,[status(thm)],[262,theory(equality)]) ).

cnf(264,negated_conjecture,
    ( cons(X2,nil) != X1
    | hd(esk7_0) != X2
    | ~ neq(nil,esk7_0)
    | ~ ssItem(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[263,235]) ).

cnf(265,negated_conjecture,
    ( nil = esk7_0
    | cons(X1,nil) != X2
    | hd(esk7_0) != X1
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(esk7_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[264,106,theory(equality)]) ).

cnf(267,negated_conjecture,
    ( nil = esk7_0
    | cons(X1,nil) != X2
    | hd(esk7_0) != X1
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | $false
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[265,129,theory(equality)]) ).

cnf(268,negated_conjecture,
    ( nil = esk7_0
    | cons(X1,nil) != X2
    | hd(esk7_0) != X1
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | $false
    | $false ),
    inference(rw,[status(thm)],[267,112,theory(equality)]) ).

cnf(269,negated_conjecture,
    ( nil = esk7_0
    | cons(X1,nil) != X2
    | hd(esk7_0) != X1
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[268,theory(equality)]) ).

cnf(276,negated_conjecture,
    ( esk7_0 = nil
    | cons(hd(esk7_0),nil) != X1
    | ~ ssItem(hd(esk7_0))
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[269,theory(equality)]) ).

cnf(307,negated_conjecture,
    ( esk7_0 = nil
    | cons(hd(esk7_0),nil) != X1
    | ~ ssList(X1)
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[276,80,theory(equality)]) ).

cnf(308,negated_conjecture,
    ( esk7_0 = nil
    | cons(hd(esk7_0),nil) != X1
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[307,129,theory(equality)]) ).

cnf(309,negated_conjecture,
    ( esk7_0 = nil
    | cons(hd(esk7_0),nil) != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[308,theory(equality)]) ).

cnf(310,negated_conjecture,
    ( esk7_0 = nil
    | ~ ssList(cons(hd(esk7_0),nil)) ),
    inference(er,[status(thm)],[309,theory(equality)]) ).

cnf(311,negated_conjecture,
    ( esk7_0 = nil
    | ~ ssItem(hd(esk7_0))
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[310,111,theory(equality)]) ).

cnf(312,negated_conjecture,
    ( esk7_0 = nil
    | ~ ssItem(hd(esk7_0))
    | $false ),
    inference(rw,[status(thm)],[311,112,theory(equality)]) ).

cnf(313,negated_conjecture,
    ( esk7_0 = nil
    | ~ ssItem(hd(esk7_0)) ),
    inference(cn,[status(thm)],[312,theory(equality)]) ).

cnf(314,negated_conjecture,
    ( esk7_0 = nil
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[313,80,theory(equality)]) ).

cnf(315,negated_conjecture,
    ( esk7_0 = nil
    | $false ),
    inference(rw,[status(thm)],[314,129,theory(equality)]) ).

cnf(316,negated_conjecture,
    esk7_0 = nil,
    inference(cn,[status(thm)],[315,theory(equality)]) ).

cnf(317,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[135,316,theory(equality)]) ).

cnf(332,negated_conjecture,
    ~ ssList(nil),
    inference(spm,[status(thm)],[158,317,theory(equality)]) ).

cnf(334,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[332,112,theory(equality)]) ).

cnf(335,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[334,theory(equality)]) ).

cnf(336,negated_conjecture,
    $false,
    335,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC013+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpah920q/sel_SWC013+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC013+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC013+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC013+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
% 
%------------------------------------------------------------------------------