TSTP Solution File: SWC320+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC320+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 11:27:49 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   51 (  11 unt;   0 def)
%            Number of atoms       :  279 ( 133 equ)
%            Maximal formula atoms :   30 (   5 avg)
%            Number of connectives :  354 ( 126   ~; 125   |;  88   &)
%                                         (   1 <=>;  14  =>;   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;   7 con; 0-2 aty)
%            Number of variables   :   65 (   0 sgn  38   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmp_L_sNY/sel_SWC320+1.p_1',ax15) ).

fof(12,axiom,
    ssList(nil),
    file('/tmp/tmp_L_sNY/sel_SWC320+1.p_1',ax17) ).

fof(19,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ~ ssList(X4)
                  | X2 != X4
                  | X1 != X3
                  | ( nil != X3
                    & nil = X4 )
                  | ( ! [X5] :
                        ( ssItem(X5)
                       => ! [X6] :
                            ( ~ ssList(X6)
                            | app(cons(X5,nil),X6) != X3
                            | app(X6,cons(X5,nil)) != X4 ) )
                    & neq(X4,nil) )
                  | ( ( nil != X2
                      | nil = X1 )
                    & ( ~ neq(X2,nil)
                      | ? [X7] :
                          ( ssItem(X7)
                          & ? [X8] :
                              ( ssList(X8)
                              & app(cons(X7,nil),X8) = X1
                              & app(X8,cons(X7,nil)) = X2 ) ) ) ) ) ) ) ),
    file('/tmp/tmp_L_sNY/sel_SWC320+1.p_1',co1) ).

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

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
                  & ( nil = X3
                    | nil != X4 )
                  & ( ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & app(cons(X5,nil),X6) = X3
                            & app(X6,cons(X5,nil)) = X4 ) )
                    | ~ neq(X4,nil) )
                  & ( ( nil = X2
                      & nil != X1 )
                    | ( neq(X2,nil)
                      & ! [X7] :
                          ( ~ ssItem(X7)
                          | ! [X8] :
                              ( ~ ssList(X8)
                              | app(cons(X7,nil),X8) != X1
                              | app(X8,cons(X7,nil)) != X2 ) ) ) ) ) ) ) ),
    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
                  & ( nil = X11
                    | nil != X12 )
                  & ( ? [X13] :
                        ( ssItem(X13)
                        & ? [X14] :
                            ( ssList(X14)
                            & app(cons(X13,nil),X14) = X11
                            & app(X14,cons(X13,nil)) = X12 ) )
                    | ~ neq(X12,nil) )
                  & ( ( nil = X10
                      & nil != X9 )
                    | ( neq(X10,nil)
                      & ! [X15] :
                          ( ~ ssItem(X15)
                          | ! [X16] :
                              ( ~ ssList(X16)
                              | app(cons(X15,nil),X16) != X9
                              | app(X16,cons(X15,nil)) != X10 ) ) ) ) ) ) ) ),
    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
    & ( nil = esk7_0
      | nil != esk8_0 )
    & ( ( ssItem(esk9_0)
        & ssList(esk10_0)
        & app(cons(esk9_0,nil),esk10_0) = esk7_0
        & app(esk10_0,cons(esk9_0,nil)) = esk8_0 )
      | ~ neq(esk8_0,nil) )
    & ( ( nil = esk6_0
        & nil != esk5_0 )
      | ( neq(esk6_0,nil)
        & ! [X15] :
            ( ~ ssItem(X15)
            | ! [X16] :
                ( ~ ssList(X16)
                | app(cons(X15,nil),X16) != esk5_0
                | app(X16,cons(X15,nil)) != esk6_0 ) ) ) ) ),
    inference(skolemize,[status(esa)],[103]) ).

fof(105,negated_conjecture,
    ! [X15,X16] :
      ( ( ( ( ~ ssList(X16)
            | app(cons(X15,nil),X16) != esk5_0
            | app(X16,cons(X15,nil)) != esk6_0
            | ~ ssItem(X15) )
          & neq(esk6_0,nil) )
        | ( nil = esk6_0
          & nil != esk5_0 ) )
      & ssList(esk8_0)
      & esk6_0 = esk8_0
      & esk5_0 = esk7_0
      & ( nil = esk7_0
        | nil != esk8_0 )
      & ( ( ssItem(esk9_0)
          & ssList(esk10_0)
          & app(cons(esk9_0,nil),esk10_0) = esk7_0
          & app(esk10_0,cons(esk9_0,nil)) = esk8_0 )
        | ~ neq(esk8_0,nil) )
      & ssList(esk7_0)
      & ssList(esk6_0)
      & ssList(esk5_0) ),
    inference(shift_quantors,[status(thm)],[104]) ).

fof(106,negated_conjecture,
    ! [X15,X16] :
      ( ( nil = esk6_0
        | ~ ssList(X16)
        | app(cons(X15,nil),X16) != esk5_0
        | app(X16,cons(X15,nil)) != esk6_0
        | ~ ssItem(X15) )
      & ( nil != esk5_0
        | ~ ssList(X16)
        | app(cons(X15,nil),X16) != esk5_0
        | app(X16,cons(X15,nil)) != esk6_0
        | ~ ssItem(X15) )
      & ( nil = esk6_0
        | neq(esk6_0,nil) )
      & ( nil != esk5_0
        | neq(esk6_0,nil) )
      & ssList(esk8_0)
      & esk6_0 = esk8_0
      & esk5_0 = esk7_0
      & ( nil = esk7_0
        | nil != esk8_0 )
      & ( ssItem(esk9_0)
        | ~ neq(esk8_0,nil) )
      & ( ssList(esk10_0)
        | ~ neq(esk8_0,nil) )
      & ( app(cons(esk9_0,nil),esk10_0) = esk7_0
        | ~ neq(esk8_0,nil) )
      & ( app(esk10_0,cons(esk9_0,nil)) = esk8_0
        | ~ neq(esk8_0,nil) )
      & ssList(esk7_0)
      & ssList(esk6_0)
      & ssList(esk5_0) ),
    inference(distribute,[status(thm)],[105]) ).

cnf(110,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = esk8_0
    | ~ neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(111,negated_conjecture,
    ( app(cons(esk9_0,nil),esk10_0) = esk7_0
    | ~ neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(112,negated_conjecture,
    ( ssList(esk10_0)
    | ~ neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(113,negated_conjecture,
    ( ssItem(esk9_0)
    | ~ neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(114,negated_conjecture,
    ( nil = esk7_0
    | nil != esk8_0 ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(115,negated_conjecture,
    esk5_0 = esk7_0,
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(116,negated_conjecture,
    esk6_0 = esk8_0,
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(118,negated_conjecture,
    ( neq(esk6_0,nil)
    | nil != esk5_0 ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(119,negated_conjecture,
    ( neq(esk6_0,nil)
    | nil = esk6_0 ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(121,negated_conjecture,
    ( nil = esk6_0
    | ~ ssItem(X1)
    | app(X2,cons(X1,nil)) != esk6_0
    | app(cons(X1,nil),X2) != esk5_0
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(125,negated_conjecture,
    ( esk5_0 = nil
    | esk8_0 != nil ),
    inference(rw,[status(thm)],[114,115,theory(equality)]) ).

cnf(126,negated_conjecture,
    ( esk8_0 = nil
    | neq(esk6_0,nil) ),
    inference(rw,[status(thm)],[119,116,theory(equality)]) ).

cnf(127,negated_conjecture,
    ( esk8_0 = nil
    | neq(esk8_0,nil) ),
    inference(rw,[status(thm)],[126,116,theory(equality)]) ).

cnf(128,negated_conjecture,
    ( ssItem(esk9_0)
    | esk8_0 = nil ),
    inference(spm,[status(thm)],[113,127,theory(equality)]) ).

cnf(129,negated_conjecture,
    ( ssList(esk10_0)
    | esk8_0 = nil ),
    inference(spm,[status(thm)],[112,127,theory(equality)]) ).

cnf(130,negated_conjecture,
    ( neq(esk8_0,nil)
    | esk5_0 != nil ),
    inference(rw,[status(thm)],[118,116,theory(equality)]) ).

cnf(137,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = esk8_0
    | esk8_0 = nil ),
    inference(spm,[status(thm)],[110,127,theory(equality)]) ).

cnf(138,negated_conjecture,
    ( app(cons(esk9_0,nil),esk10_0) = esk5_0
    | ~ neq(esk8_0,nil) ),
    inference(rw,[status(thm)],[111,115,theory(equality)]) ).

cnf(139,negated_conjecture,
    ( app(cons(esk9_0,nil),esk10_0) = esk5_0
    | esk8_0 = nil ),
    inference(spm,[status(thm)],[138,127,theory(equality)]) ).

cnf(157,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[69,theory(equality)]) ).

cnf(243,negated_conjecture,
    ( esk8_0 = nil
    | app(X2,cons(X1,nil)) != esk6_0
    | app(cons(X1,nil),X2) != esk5_0
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[121,116,theory(equality)]) ).

cnf(244,negated_conjecture,
    ( esk8_0 = nil
    | app(X2,cons(X1,nil)) != esk8_0
    | app(cons(X1,nil),X2) != esk5_0
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[243,116,theory(equality)]) ).

cnf(284,negated_conjecture,
    ( esk8_0 = nil
    | app(cons(esk9_0,nil),esk10_0) != esk5_0
    | ~ ssList(esk10_0)
    | ~ ssItem(esk9_0) ),
    inference(spm,[status(thm)],[244,137,theory(equality)]) ).

cnf(436,negated_conjecture,
    ( esk8_0 = nil
    | app(cons(esk9_0,nil),esk10_0) != esk5_0
    | ~ ssList(esk10_0) ),
    inference(csr,[status(thm)],[284,128]) ).

cnf(437,negated_conjecture,
    ( esk8_0 = nil
    | app(cons(esk9_0,nil),esk10_0) != esk5_0 ),
    inference(csr,[status(thm)],[436,129]) ).

cnf(438,negated_conjecture,
    esk8_0 = nil,
    inference(csr,[status(thm)],[437,139]) ).

cnf(464,negated_conjecture,
    ( neq(nil,nil)
    | esk5_0 != nil ),
    inference(rw,[status(thm)],[130,438,theory(equality)]) ).

cnf(467,negated_conjecture,
    ( esk5_0 = nil
    | $false ),
    inference(rw,[status(thm)],[125,438,theory(equality)]) ).

cnf(468,negated_conjecture,
    esk5_0 = nil,
    inference(cn,[status(thm)],[467,theory(equality)]) ).

cnf(503,negated_conjecture,
    ( neq(nil,nil)
    | $false ),
    inference(rw,[status(thm)],[464,468,theory(equality)]) ).

cnf(504,negated_conjecture,
    neq(nil,nil),
    inference(cn,[status(thm)],[503,theory(equality)]) ).

cnf(506,negated_conjecture,
    ~ ssList(nil),
    inference(spm,[status(thm)],[157,504,theory(equality)]) ).

cnf(511,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[506,74,theory(equality)]) ).

cnf(512,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[511,theory(equality)]) ).

cnf(513,negated_conjecture,
    $false,
    512,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC320+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp_L_sNY/sel_SWC320+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC320+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC320+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC320+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
% 
%------------------------------------------------------------------------------