TSTP Solution File: SWC353+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC353+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 11:37:34 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   35 (  11 unt;   0 def)
%            Number of atoms       :  229 (  64 equ)
%            Maximal formula atoms :   19 (   6 avg)
%            Number of connectives :  301 ( 107   ~;  98   |;  76   &)
%                                         (   1 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   90 (   0 sgn  56   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmplBu81G/sel_SWC353+1.p_1',ax26) ).

fof(23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/tmp/tmplBu81G/sel_SWC353+1.p_1',ax5) ).

fof(36,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssList(X5)
                       => ( app(X3,X5) != X4
                          | ~ totalorderedP(X3)
                          | ? [X6] :
                              ( ssItem(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(cons(X6,nil),X7) = X5
                                  & ? [X8] :
                                      ( ssItem(X8)
                                      & ? [X9] :
                                          ( ssList(X9)
                                          & app(X9,cons(X8,nil)) = X3
                                          & leq(X8,X6) ) ) ) ) ) )
                    | frontsegP(X2,X1)
                    | ( nil != X4
                      & nil = X3 ) ) ) ) ) ),
    file('/tmp/tmplBu81G/sel_SWC353+1.p_1',co1) ).

fof(37,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssList(X5)
                         => ( app(X3,X5) != X4
                            | ~ totalorderedP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssItem(X8)
                                        & ? [X9] :
                                            ( ssList(X9)
                                            & app(X9,cons(X8,nil)) = X3
                                            & leq(X8,X6) ) ) ) ) ) )
                      | frontsegP(X2,X1)
                      | ( nil != X4
                        & nil = X3 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[36]) ).

fof(38,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssList(X5)
                         => ( app(X3,X5) != X4
                            | ~ totalorderedP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssItem(X8)
                                        & ? [X9] :
                                            ( ssList(X9)
                                            & app(X9,cons(X8,nil)) = X3
                                            & leq(X8,X6) ) ) ) ) ) )
                      | frontsegP(X2,X1)
                      | ( nil != X4
                        & nil = X3 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[37,theory(equality)]) ).

fof(100,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(101,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[100]) ).

fof(102,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ssList(app(X3,X4))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[101]) ).

cnf(103,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[102]) ).

fof(133,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ frontsegP(X1,X2)
              | ? [X3] :
                  ( ssList(X3)
                  & app(X2,X3) = X1 ) )
            & ( ! [X3] :
                  ( ~ ssList(X3)
                  | app(X2,X3) != X1 )
              | frontsegP(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(134,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ( ( ~ frontsegP(X4,X5)
              | ? [X6] :
                  ( ssList(X6)
                  & app(X5,X6) = X4 ) )
            & ( ! [X7] :
                  ( ~ ssList(X7)
                  | app(X5,X7) != X4 )
              | frontsegP(X4,X5) ) ) ) ),
    inference(variable_rename,[status(thm)],[133]) ).

fof(135,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ( ( ~ frontsegP(X4,X5)
              | ( ssList(esk3_2(X4,X5))
                & app(X5,esk3_2(X4,X5)) = X4 ) )
            & ( ! [X7] :
                  ( ~ ssList(X7)
                  | app(X5,X7) != X4 )
              | frontsegP(X4,X5) ) ) ) ),
    inference(skolemize,[status(esa)],[134]) ).

fof(136,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ ssList(X7)
          | app(X5,X7) != X4
          | frontsegP(X4,X5) )
        & ( ~ frontsegP(X4,X5)
          | ( ssList(esk3_2(X4,X5))
            & app(X5,esk3_2(X4,X5)) = X4 ) ) )
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[135]) ).

fof(137,plain,
    ! [X4,X5,X7] :
      ( ( ~ ssList(X7)
        | app(X5,X7) != X4
        | frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( ssList(esk3_2(X4,X5))
        | ~ frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( app(X5,esk3_2(X4,X5)) = X4
        | ~ frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[136]) ).

cnf(140,plain,
    ( frontsegP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X2,X3) != X1
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[137]) ).

fof(199,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ? [X5] :
                      ( ssList(X5)
                      & app(X3,X5) = X4
                      & totalorderedP(X3)
                      & ! [X6] :
                          ( ~ ssItem(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(cons(X6,nil),X7) != X5
                              | ! [X8] :
                                  ( ~ ssItem(X8)
                                  | ! [X9] :
                                      ( ~ ssList(X9)
                                      | app(X9,cons(X8,nil)) != X3
                                      | ~ leq(X8,X6) ) ) ) ) )
                  & ~ frontsegP(X2,X1)
                  & ( nil = X4
                    | nil != X3 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(200,negated_conjecture,
    ? [X10] :
      ( ssList(X10)
      & ? [X11] :
          ( ssList(X11)
          & ? [X12] :
              ( ssList(X12)
              & ? [X13] :
                  ( ssList(X13)
                  & X11 = X13
                  & X10 = X12
                  & ? [X14] :
                      ( ssList(X14)
                      & app(X12,X14) = X13
                      & totalorderedP(X12)
                      & ! [X15] :
                          ( ~ ssItem(X15)
                          | ! [X16] :
                              ( ~ ssList(X16)
                              | app(cons(X15,nil),X16) != X14
                              | ! [X17] :
                                  ( ~ ssItem(X17)
                                  | ! [X18] :
                                      ( ~ ssList(X18)
                                      | app(X18,cons(X17,nil)) != X12
                                      | ~ leq(X17,X15) ) ) ) ) )
                  & ~ frontsegP(X11,X10)
                  & ( nil = X13
                    | nil != X12 ) ) ) ) ),
    inference(variable_rename,[status(thm)],[199]) ).

fof(201,negated_conjecture,
    ( ssList(esk12_0)
    & ssList(esk13_0)
    & ssList(esk14_0)
    & ssList(esk15_0)
    & esk13_0 = esk15_0
    & esk12_0 = esk14_0
    & ssList(esk16_0)
    & app(esk14_0,esk16_0) = esk15_0
    & totalorderedP(esk14_0)
    & ! [X15] :
        ( ~ ssItem(X15)
        | ! [X16] :
            ( ~ ssList(X16)
            | app(cons(X15,nil),X16) != esk16_0
            | ! [X17] :
                ( ~ ssItem(X17)
                | ! [X18] :
                    ( ~ ssList(X18)
                    | app(X18,cons(X17,nil)) != esk14_0
                    | ~ leq(X17,X15) ) ) ) )
    & ~ frontsegP(esk13_0,esk12_0)
    & ( nil = esk15_0
      | nil != esk14_0 ) ),
    inference(skolemize,[status(esa)],[200]) ).

fof(202,negated_conjecture,
    ! [X15,X16,X17,X18] :
      ( ( ~ ssList(X18)
        | app(X18,cons(X17,nil)) != esk14_0
        | ~ leq(X17,X15)
        | ~ ssItem(X17)
        | ~ ssList(X16)
        | app(cons(X15,nil),X16) != esk16_0
        | ~ ssItem(X15) )
      & app(esk14_0,esk16_0) = esk15_0
      & totalorderedP(esk14_0)
      & ssList(esk16_0)
      & esk13_0 = esk15_0
      & esk12_0 = esk14_0
      & ~ frontsegP(esk13_0,esk12_0)
      & ( nil = esk15_0
        | nil != esk14_0 )
      & ssList(esk15_0)
      & ssList(esk14_0)
      & ssList(esk13_0)
      & ssList(esk12_0) ),
    inference(shift_quantors,[status(thm)],[201]) ).

cnf(203,negated_conjecture,
    ssList(esk12_0),
    inference(split_conjunct,[status(thm)],[202]) ).

cnf(208,negated_conjecture,
    ~ frontsegP(esk13_0,esk12_0),
    inference(split_conjunct,[status(thm)],[202]) ).

cnf(209,negated_conjecture,
    esk12_0 = esk14_0,
    inference(split_conjunct,[status(thm)],[202]) ).

cnf(210,negated_conjecture,
    esk13_0 = esk15_0,
    inference(split_conjunct,[status(thm)],[202]) ).

cnf(211,negated_conjecture,
    ssList(esk16_0),
    inference(split_conjunct,[status(thm)],[202]) ).

cnf(213,negated_conjecture,
    app(esk14_0,esk16_0) = esk15_0,
    inference(split_conjunct,[status(thm)],[202]) ).

cnf(215,negated_conjecture,
    ssList(esk14_0),
    inference(rw,[status(thm)],[203,209,theory(equality)]) ).

cnf(217,negated_conjecture,
    ~ frontsegP(esk15_0,esk14_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[208,210,theory(equality)]),209,theory(equality)]) ).

cnf(257,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(app(X1,X2)) ),
    inference(er,[status(thm)],[140,theory(equality)]) ).

cnf(562,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[257,103]) ).

cnf(563,negated_conjecture,
    ( frontsegP(esk15_0,esk14_0)
    | ~ ssList(esk16_0)
    | ~ ssList(esk14_0) ),
    inference(spm,[status(thm)],[562,213,theory(equality)]) ).

cnf(575,negated_conjecture,
    ( frontsegP(esk15_0,esk14_0)
    | ~ ssList(esk16_0)
    | $false ),
    inference(rw,[status(thm)],[563,215,theory(equality)]) ).

cnf(576,negated_conjecture,
    ( frontsegP(esk15_0,esk14_0)
    | ~ ssList(esk16_0) ),
    inference(cn,[status(thm)],[575,theory(equality)]) ).

cnf(577,negated_conjecture,
    ~ ssList(esk16_0),
    inference(sr,[status(thm)],[576,217,theory(equality)]) ).

cnf(587,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[211,577,theory(equality)]) ).

cnf(588,negated_conjecture,
    $false,
    587,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC353+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmplBu81G/sel_SWC353+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC353+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC353+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC353+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
% 
%------------------------------------------------------------------------------