TSTP Solution File: SWC309+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC309+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 11:23:04 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   51 (  13 unt;   0 def)
%            Number of atoms       :  259 ( 108 equ)
%            Maximal formula atoms :   17 (   5 avg)
%            Number of connectives :  331 ( 123   ~; 119   |;  71   &)
%                                         (   1 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  100 (   0 sgn  51   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmplp7GTZ/sel_SWC309+1.p_1',ax81) ).

fof(9,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/tmp/tmplp7GTZ/sel_SWC309+1.p_1',ax20) ).

fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmplp7GTZ/sel_SWC309+1.p_1',ax15) ).

fof(12,axiom,
    ssList(nil),
    file('/tmp/tmplp7GTZ/sel_SWC309+1.p_1',ax17) ).

fof(19,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ neq(X2,nil)
                    | ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & app(cons(X5,nil),X6) = X2
                            & app(X6,cons(X5,nil)) = X1 ) )
                    | ? [X7] :
                        ( ssItem(X7)
                        & ? [X8] :
                            ( ssList(X8)
                            & app(X8,cons(X7,nil)) != X3
                            & app(cons(X7,nil),X8) = X4 ) )
                    | ( nil != X3
                      & nil = X4 ) ) ) ) ) ),
    file('/tmp/tmplp7GTZ/sel_SWC309+1.p_1',co1) ).

fof(20,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ neq(X2,nil)
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & app(cons(X5,nil),X6) = X2
                              & app(X6,cons(X5,nil)) = X1 ) )
                      | ? [X7] :
                          ( ssItem(X7)
                          & ? [X8] :
                              ( ssList(X8)
                              & app(X8,cons(X7,nil)) != X3
                              & app(cons(X7,nil),X8) = X4 ) )
                      | ( nil != X3
                        & nil = X4 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[19]) ).

fof(21,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ neq(X2,nil)
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & app(cons(X5,nil),X6) = X2
                              & app(X6,cons(X5,nil)) = X1 ) )
                      | ? [X7] :
                          ( ssItem(X7)
                          & ? [X8] :
                              ( ssList(X8)
                              & app(X8,cons(X7,nil)) != X3
                              & app(cons(X7,nil),X8) = X4 ) )
                      | ( nil != X3
                        & nil = X4 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[20,theory(equality)]) ).

fof(53,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(54,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) = app(cons(X4,nil),X3) ) ),
    inference(variable_rename,[status(thm)],[53]) ).

fof(55,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) = app(cons(X4,nil),X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[54]) ).

cnf(56,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(57,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssItem(X3)
              & cons(X3,X2) = X1 ) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(58,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ? [X5] :
          ( ssList(X5)
          & ? [X6] :
              ( ssItem(X6)
              & cons(X6,X5) = X4 ) ) ),
    inference(variable_rename,[status(thm)],[57]) ).

fof(59,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ( ssList(esk3_1(X4))
        & ssItem(esk4_1(X4))
        & cons(esk4_1(X4),esk3_1(X4)) = X4 ) ),
    inference(skolemize,[status(esa)],[58]) ).

fof(60,plain,
    ! [X4] :
      ( ( ssList(esk3_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( ssItem(esk4_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( cons(esk4_1(X4),esk3_1(X4)) = X4
        | nil = X4
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[59]) ).

cnf(61,plain,
    ( nil = X1
    | cons(esk4_1(X1),esk3_1(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[60]) ).

cnf(62,plain,
    ( nil = X1
    | ssItem(esk4_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[60]) ).

cnf(63,plain,
    ( nil = X1
    | ssList(esk3_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[60]) ).

fof(64,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(65,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[64]) ).

fof(66,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[65]) ).

fof(67,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)],[66]) ).

cnf(69,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | X1 != X2
    | ~ neq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(74,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(102,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & neq(X2,nil)
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | app(cons(X5,nil),X6) != X2
                          | app(X6,cons(X5,nil)) != X1 ) )
                  & ! [X7] :
                      ( ~ ssItem(X7)
                      | ! [X8] :
                          ( ~ ssList(X8)
                          | app(X8,cons(X7,nil)) = X3
                          | app(cons(X7,nil),X8) != X4 ) )
                  & ( nil = X3
                    | nil != X4 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(103,negated_conjecture,
    ? [X9] :
      ( ssList(X9)
      & ? [X10] :
          ( ssList(X10)
          & ? [X11] :
              ( ssList(X11)
              & ? [X12] :
                  ( ssList(X12)
                  & X10 = X12
                  & X9 = X11
                  & neq(X10,nil)
                  & ! [X13] :
                      ( ~ ssItem(X13)
                      | ! [X14] :
                          ( ~ ssList(X14)
                          | app(cons(X13,nil),X14) != X10
                          | app(X14,cons(X13,nil)) != X9 ) )
                  & ! [X15] :
                      ( ~ ssItem(X15)
                      | ! [X16] :
                          ( ~ ssList(X16)
                          | app(X16,cons(X15,nil)) = X11
                          | app(cons(X15,nil),X16) != X12 ) )
                  & ( nil = X11
                    | nil != X12 ) ) ) ) ),
    inference(variable_rename,[status(thm)],[102]) ).

fof(104,negated_conjecture,
    ( ssList(esk5_0)
    & ssList(esk6_0)
    & ssList(esk7_0)
    & ssList(esk8_0)
    & esk6_0 = esk8_0
    & esk5_0 = esk7_0
    & neq(esk6_0,nil)
    & ! [X13] :
        ( ~ ssItem(X13)
        | ! [X14] :
            ( ~ ssList(X14)
            | app(cons(X13,nil),X14) != esk6_0
            | app(X14,cons(X13,nil)) != esk5_0 ) )
    & ! [X15] :
        ( ~ ssItem(X15)
        | ! [X16] :
            ( ~ ssList(X16)
            | app(X16,cons(X15,nil)) = esk7_0
            | app(cons(X15,nil),X16) != esk8_0 ) )
    & ( nil = esk7_0
      | nil != esk8_0 ) ),
    inference(skolemize,[status(esa)],[103]) ).

fof(105,negated_conjecture,
    ! [X13,X14,X15,X16] :
      ( ( ~ ssList(X16)
        | app(X16,cons(X15,nil)) = esk7_0
        | app(cons(X15,nil),X16) != esk8_0
        | ~ ssItem(X15) )
      & ( ~ ssList(X14)
        | app(cons(X13,nil),X14) != esk6_0
        | app(X14,cons(X13,nil)) != esk5_0
        | ~ ssItem(X13) )
      & esk6_0 = esk8_0
      & esk5_0 = esk7_0
      & neq(esk6_0,nil)
      & ( nil = esk7_0
        | nil != esk8_0 )
      & ssList(esk8_0)
      & ssList(esk7_0)
      & ssList(esk6_0)
      & ssList(esk5_0) ),
    inference(shift_quantors,[status(thm)],[104]) ).

cnf(109,negated_conjecture,
    ssList(esk8_0),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(111,negated_conjecture,
    neq(esk6_0,nil),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(112,negated_conjecture,
    esk5_0 = esk7_0,
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(113,negated_conjecture,
    esk6_0 = esk8_0,
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(114,negated_conjecture,
    ( ~ ssItem(X1)
    | app(X2,cons(X1,nil)) != esk5_0
    | app(cons(X1,nil),X2) != esk6_0
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(115,negated_conjecture,
    ( app(X2,cons(X1,nil)) = esk7_0
    | ~ ssItem(X1)
    | app(cons(X1,nil),X2) != esk8_0
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(118,negated_conjecture,
    neq(esk8_0,nil),
    inference(rw,[status(thm)],[111,113,theory(equality)]) ).

cnf(138,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[69,theory(equality)]) ).

cnf(216,negated_conjecture,
    ( app(X2,cons(X1,nil)) != esk7_0
    | app(cons(X1,nil),X2) != esk6_0
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[114,112,theory(equality)]) ).

cnf(217,negated_conjecture,
    ( app(X2,cons(X1,nil)) != esk7_0
    | app(cons(X1,nil),X2) != esk8_0
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[216,113,theory(equality)]) ).

cnf(218,negated_conjecture,
    ( app(cons(X1,nil),X2) != esk8_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[217,115]) ).

cnf(220,negated_conjecture,
    ( cons(X1,X2) != esk8_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[218,56,theory(equality)]) ).

cnf(227,negated_conjecture,
    ( nil = X1
    | X1 != esk8_0
    | ~ ssList(esk3_1(X1))
    | ~ ssItem(esk4_1(X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[220,61,theory(equality)]) ).

cnf(258,negated_conjecture,
    ( nil = X1
    | X1 != esk8_0
    | ~ ssList(esk3_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[227,62]) ).

cnf(259,negated_conjecture,
    ( nil = X1
    | X1 != esk8_0
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[258,63]) ).

cnf(260,negated_conjecture,
    ( nil = esk8_0
    | ~ ssList(esk8_0) ),
    inference(er,[status(thm)],[259,theory(equality)]) ).

cnf(261,negated_conjecture,
    ( nil = esk8_0
    | $false ),
    inference(rw,[status(thm)],[260,109,theory(equality)]) ).

cnf(262,negated_conjecture,
    nil = esk8_0,
    inference(cn,[status(thm)],[261,theory(equality)]) ).

cnf(263,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[118,262,theory(equality)]) ).

cnf(279,negated_conjecture,
    ~ ssList(nil),
    inference(spm,[status(thm)],[138,263,theory(equality)]) ).

cnf(280,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[279,74,theory(equality)]) ).

cnf(281,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[280,theory(equality)]) ).

cnf(282,negated_conjecture,
    $false,
    281,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC309+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmplp7GTZ/sel_SWC309+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC309+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC309+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC309+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
% 
%------------------------------------------------------------------------------