TSTP Solution File: SWC355+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC355+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 11:37:47 EST 2010

% Result   : Theorem 0.32s
% Output   : CNFRefutation 0.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   56 (  12 unt;   0 def)
%            Number of atoms       :  270 (  55 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  340 ( 126   ~; 130   |;  63   &)
%                                         (   1 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   87 (   0 sgn  48   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpKEZ3Gs/sel_SWC355+1.p_1',ax28) ).

fof(13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/tmp/tmpKEZ3Gs/sel_SWC355+1.p_1',ax7) ).

fof(19,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpKEZ3Gs/sel_SWC355+1.p_1',ax16) ).

fof(20,axiom,
    ssList(nil),
    file('/tmp/tmpKEZ3Gs/sel_SWC355+1.p_1',ax17) ).

fof(26,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ( ~ neq(X2,nil)
                        | ! [X5] :
                            ( ssItem(X5)
                           => app(X3,cons(X5,nil)) != X4 )
                        | segmentP(X2,X1) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/tmp/tmpKEZ3Gs/sel_SWC355+1.p_1',co1) ).

fof(27,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ! [X5] :
                              ( ssItem(X5)
                             => app(X3,cons(X5,nil)) != X4 )
                          | segmentP(X2,X1) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[26]) ).

fof(28,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ! [X5] :
                              ( ssItem(X5)
                             => app(X3,cons(X5,nil)) != X4 )
                          | segmentP(X2,X1) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[27,theory(equality)]) ).

fof(51,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(52,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[51]) ).

cnf(53,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(84,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ segmentP(X1,X2)
              | ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ssList(X4)
                      & app(app(X3,X2),X4) = X1 ) ) )
            & ( ! [X3] :
                  ( ~ ssList(X3)
                  | ! [X4] :
                      ( ~ ssList(X4)
                      | app(app(X3,X2),X4) != X1 ) )
              | segmentP(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(85,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssList(X6)
          | ( ( ~ segmentP(X5,X6)
              | ? [X7] :
                  ( ssList(X7)
                  & ? [X8] :
                      ( ssList(X8)
                      & app(app(X7,X6),X8) = X5 ) ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(app(X9,X6),X10) != X5 ) )
              | segmentP(X5,X6) ) ) ) ),
    inference(variable_rename,[status(thm)],[84]) ).

fof(86,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssList(X6)
          | ( ( ~ segmentP(X5,X6)
              | ( ssList(esk5_2(X5,X6))
                & ssList(esk6_2(X5,X6))
                & app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(app(X9,X6),X10) != X5 ) )
              | segmentP(X5,X6) ) ) ) ),
    inference(skolemize,[status(esa)],[85]) ).

fof(87,plain,
    ! [X5,X6,X9,X10] :
      ( ( ( ~ ssList(X10)
          | app(app(X9,X6),X10) != X5
          | ~ ssList(X9)
          | segmentP(X5,X6) )
        & ( ~ segmentP(X5,X6)
          | ( ssList(esk5_2(X5,X6))
            & ssList(esk6_2(X5,X6))
            & app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) ) )
      | ~ ssList(X6)
      | ~ ssList(X5) ),
    inference(shift_quantors,[status(thm)],[86]) ).

fof(88,plain,
    ! [X5,X6,X9,X10] :
      ( ( ~ ssList(X10)
        | app(app(X9,X6),X10) != X5
        | ~ ssList(X9)
        | segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ssList(esk5_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ssList(esk6_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) ) ),
    inference(distribute,[status(thm)],[87]) ).

cnf(92,plain,
    ( segmentP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X3,X2),X4) != X1
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[88]) ).

fof(118,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(119,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[118]) ).

fof(120,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[119]) ).

cnf(121,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[120]) ).

cnf(122,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(141,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ( neq(X2,nil)
                      & ? [X5] :
                          ( ssItem(X5)
                          & app(X3,cons(X5,nil)) = X4 )
                      & ~ segmentP(X2,X1) )
                    | ( neq(X2,nil)
                      & ~ neq(X4,nil) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(142,negated_conjecture,
    ? [X6] :
      ( ssList(X6)
      & ? [X7] :
          ( ssList(X7)
          & ? [X8] :
              ( ssList(X8)
              & ? [X9] :
                  ( ssList(X9)
                  & X7 = X9
                  & X6 = X8
                  & ( ( neq(X7,nil)
                      & ? [X10] :
                          ( ssItem(X10)
                          & app(X8,cons(X10,nil)) = X9 )
                      & ~ segmentP(X7,X6) )
                    | ( neq(X7,nil)
                      & ~ neq(X9,nil) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[141]) ).

fof(143,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & ( ( neq(esk8_0,nil)
        & ssItem(esk11_0)
        & app(esk9_0,cons(esk11_0,nil)) = esk10_0
        & ~ segmentP(esk8_0,esk7_0) )
      | ( neq(esk8_0,nil)
        & ~ neq(esk10_0,nil) ) ) ),
    inference(skolemize,[status(esa)],[142]) ).

fof(144,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & ( neq(esk8_0,nil)
      | neq(esk8_0,nil) )
    & ( ~ neq(esk10_0,nil)
      | neq(esk8_0,nil) )
    & ( neq(esk8_0,nil)
      | ssItem(esk11_0) )
    & ( ~ neq(esk10_0,nil)
      | ssItem(esk11_0) )
    & ( neq(esk8_0,nil)
      | app(esk9_0,cons(esk11_0,nil)) = esk10_0 )
    & ( ~ neq(esk10_0,nil)
      | app(esk9_0,cons(esk11_0,nil)) = esk10_0 )
    & ( neq(esk8_0,nil)
      | ~ segmentP(esk8_0,esk7_0) )
    & ( ~ neq(esk10_0,nil)
      | ~ segmentP(esk8_0,esk7_0) ) ),
    inference(distribute,[status(thm)],[143]) ).

cnf(145,negated_conjecture,
    ( ~ segmentP(esk8_0,esk7_0)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(147,negated_conjecture,
    ( app(esk9_0,cons(esk11_0,nil)) = esk10_0
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(149,negated_conjecture,
    ( ssItem(esk11_0)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(152,negated_conjecture,
    ( neq(esk8_0,nil)
    | neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(153,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(154,negated_conjecture,
    esk8_0 = esk10_0,
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(157,negated_conjecture,
    ssList(esk8_0),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(158,negated_conjecture,
    ssList(esk7_0),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(164,negated_conjecture,
    ( ssItem(esk11_0)
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[149,154,theory(equality)]),152,theory(equality)]) ).

cnf(165,negated_conjecture,
    ssItem(esk11_0),
    inference(cn,[status(thm)],[164,theory(equality)]) ).

cnf(170,negated_conjecture,
    ( $false
    | ~ segmentP(esk8_0,esk7_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[145,154,theory(equality)]),152,theory(equality)]) ).

cnf(171,negated_conjecture,
    ~ segmentP(esk8_0,esk7_0),
    inference(cn,[status(thm)],[170,theory(equality)]) ).

cnf(178,negated_conjecture,
    ( app(esk7_0,cons(esk11_0,nil)) = esk10_0
    | ~ neq(esk10_0,nil) ),
    inference(rw,[status(thm)],[147,153,theory(equality)]) ).

cnf(179,negated_conjecture,
    ( app(esk7_0,cons(esk11_0,nil)) = esk8_0
    | ~ neq(esk10_0,nil) ),
    inference(rw,[status(thm)],[178,154,theory(equality)]) ).

cnf(180,negated_conjecture,
    ( app(esk7_0,cons(esk11_0,nil)) = esk8_0
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[179,154,theory(equality)]),152,theory(equality)]) ).

cnf(181,negated_conjecture,
    app(esk7_0,cons(esk11_0,nil)) = esk8_0,
    inference(cn,[status(thm)],[180,theory(equality)]) ).

cnf(282,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[92,53,theory(equality)]) ).

cnf(290,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[282,122,theory(equality)]) ).

cnf(291,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[290,theory(equality)]) ).

cnf(1960,negated_conjecture,
    ( segmentP(X1,esk7_0)
    | esk8_0 != X1
    | ~ ssList(cons(esk11_0,nil))
    | ~ ssList(esk7_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[291,181,theory(equality)]) ).

cnf(1972,negated_conjecture,
    ( segmentP(X1,esk7_0)
    | esk8_0 != X1
    | ~ ssList(cons(esk11_0,nil))
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1960,158,theory(equality)]) ).

cnf(1973,negated_conjecture,
    ( segmentP(X1,esk7_0)
    | esk8_0 != X1
    | ~ ssList(cons(esk11_0,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1972,theory(equality)]) ).

cnf(3969,negated_conjecture,
    ( segmentP(X1,esk7_0)
    | esk8_0 != X1
    | ~ ssList(X1)
    | ~ ssItem(esk11_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[1973,121,theory(equality)]) ).

cnf(3971,negated_conjecture,
    ( segmentP(X1,esk7_0)
    | esk8_0 != X1
    | ~ ssList(X1)
    | $false
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[3969,165,theory(equality)]) ).

cnf(3972,negated_conjecture,
    ( segmentP(X1,esk7_0)
    | esk8_0 != X1
    | ~ ssList(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3971,122,theory(equality)]) ).

cnf(3973,negated_conjecture,
    ( segmentP(X1,esk7_0)
    | esk8_0 != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[3972,theory(equality)]) ).

cnf(4001,negated_conjecture,
    ( segmentP(esk8_0,esk7_0)
    | ~ ssList(esk8_0) ),
    inference(er,[status(thm)],[3973,theory(equality)]) ).

cnf(4002,negated_conjecture,
    ( segmentP(esk8_0,esk7_0)
    | $false ),
    inference(rw,[status(thm)],[4001,157,theory(equality)]) ).

cnf(4003,negated_conjecture,
    segmentP(esk8_0,esk7_0),
    inference(cn,[status(thm)],[4002,theory(equality)]) ).

cnf(4004,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[4003,171,theory(equality)]) ).

cnf(4005,negated_conjecture,
    $false,
    4004,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC355+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpKEZ3Gs/sel_SWC355+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC355+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC355+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC355+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
% 
%------------------------------------------------------------------------------