TSTP Solution File: SWC331+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC331+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 11:30:26 EST 2010

% Result   : Theorem 0.29s
% Output   : CNFRefutation 0.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   45 (  15 unt;   0 def)
%            Number of atoms       :  263 (  75 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  344 ( 126   ~; 120   |;  79   &)
%                                         (   1 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 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   :   95 (   0 sgn  52   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmp6GV9I6/sel_SWC331+1.p_1',ax28) ).

fof(12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/tmp/tmp6GV9I6/sel_SWC331+1.p_1',ax7) ).

fof(20,axiom,
    ssList(nil),
    file('/tmp/tmp6GV9I6/sel_SWC331+1.p_1',ax17) ).

fof(27,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssList(X5)
                       => ( app(X3,X5) != X4
                          | ~ equalelemsP(X3)
                          | ? [X6] :
                              ( ssItem(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(cons(X6,nil),X7) = X5
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                    | ( nil != X4
                      & nil = X3 )
                    | ( segmentP(X2,X1)
                      & equalelemsP(X1) ) ) ) ) ) ),
    file('/tmp/tmp6GV9I6/sel_SWC331+1.p_1',co1) ).

fof(28,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
                            | ~ equalelemsP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssList(X8)
                                        & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                      | ( nil != X4
                        & nil = X3 )
                      | ( segmentP(X2,X1)
                        & equalelemsP(X1) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[27]) ).

fof(29,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
                            | ~ equalelemsP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssList(X8)
                                        & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                      | ( nil != X4
                        & nil = X3 )
                      | ( segmentP(X2,X1)
                        & equalelemsP(X1) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[28,theory(equality)]) ).

fof(52,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(53,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[52]) ).

cnf(54,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[53]) ).

fof(79,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)],[12]) ).

fof(80,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)],[79]) ).

fof(81,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)],[80]) ).

fof(82,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)],[81]) ).

fof(83,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)],[82]) ).

cnf(87,plain,
    ( segmentP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X3,X2),X4) != X1
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[83]) ).

cnf(115,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(146,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
                      & equalelemsP(X3)
                      & ! [X6] :
                          ( ~ ssItem(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(cons(X6,nil),X7) != X5
                              | ! [X8] :
                                  ( ~ ssList(X8)
                                  | app(X8,cons(X6,nil)) != X3 ) ) ) )
                  & ( nil = X4
                    | nil != X3 )
                  & ( ~ segmentP(X2,X1)
                    | ~ equalelemsP(X1) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(147,negated_conjecture,
    ? [X9] :
      ( ssList(X9)
      & ? [X10] :
          ( ssList(X10)
          & ? [X11] :
              ( ssList(X11)
              & ? [X12] :
                  ( ssList(X12)
                  & X10 = X12
                  & X9 = X11
                  & ? [X13] :
                      ( ssList(X13)
                      & app(X11,X13) = X12
                      & equalelemsP(X11)
                      & ! [X14] :
                          ( ~ ssItem(X14)
                          | ! [X15] :
                              ( ~ ssList(X15)
                              | app(cons(X14,nil),X15) != X13
                              | ! [X16] :
                                  ( ~ ssList(X16)
                                  | app(X16,cons(X14,nil)) != X11 ) ) ) )
                  & ( nil = X12
                    | nil != X11 )
                  & ( ~ segmentP(X10,X9)
                    | ~ equalelemsP(X9) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[146]) ).

fof(148,negated_conjecture,
    ( ssList(esk11_0)
    & ssList(esk12_0)
    & ssList(esk13_0)
    & ssList(esk14_0)
    & esk12_0 = esk14_0
    & esk11_0 = esk13_0
    & ssList(esk15_0)
    & app(esk13_0,esk15_0) = esk14_0
    & equalelemsP(esk13_0)
    & ! [X14] :
        ( ~ ssItem(X14)
        | ! [X15] :
            ( ~ ssList(X15)
            | app(cons(X14,nil),X15) != esk15_0
            | ! [X16] :
                ( ~ ssList(X16)
                | app(X16,cons(X14,nil)) != esk13_0 ) ) )
    & ( nil = esk14_0
      | nil != esk13_0 )
    & ( ~ segmentP(esk12_0,esk11_0)
      | ~ equalelemsP(esk11_0) ) ),
    inference(skolemize,[status(esa)],[147]) ).

fof(149,negated_conjecture,
    ! [X14,X15,X16] :
      ( ( ~ ssList(X16)
        | app(X16,cons(X14,nil)) != esk13_0
        | ~ ssList(X15)
        | app(cons(X14,nil),X15) != esk15_0
        | ~ ssItem(X14) )
      & app(esk13_0,esk15_0) = esk14_0
      & equalelemsP(esk13_0)
      & ssList(esk15_0)
      & esk12_0 = esk14_0
      & esk11_0 = esk13_0
      & ( nil = esk14_0
        | nil != esk13_0 )
      & ( ~ segmentP(esk12_0,esk11_0)
        | ~ equalelemsP(esk11_0) )
      & ssList(esk14_0)
      & ssList(esk13_0)
      & ssList(esk12_0)
      & ssList(esk11_0) ),
    inference(shift_quantors,[status(thm)],[148]) ).

cnf(150,negated_conjecture,
    ssList(esk11_0),
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(151,negated_conjecture,
    ssList(esk12_0),
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(154,negated_conjecture,
    ( ~ equalelemsP(esk11_0)
    | ~ segmentP(esk12_0,esk11_0) ),
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(156,negated_conjecture,
    esk11_0 = esk13_0,
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(157,negated_conjecture,
    esk12_0 = esk14_0,
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(158,negated_conjecture,
    ssList(esk15_0),
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(159,negated_conjecture,
    equalelemsP(esk13_0),
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(160,negated_conjecture,
    app(esk13_0,esk15_0) = esk14_0,
    inference(split_conjunct,[status(thm)],[149]) ).

cnf(162,negated_conjecture,
    ssList(esk13_0),
    inference(rw,[status(thm)],[150,156,theory(equality)]) ).

cnf(163,negated_conjecture,
    ssList(esk14_0),
    inference(rw,[status(thm)],[151,157,theory(equality)]) ).

cnf(164,negated_conjecture,
    ( $false
    | ~ segmentP(esk12_0,esk11_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[154,156,theory(equality)]),159,theory(equality)]) ).

cnf(165,negated_conjecture,
    ( $false
    | ~ segmentP(esk14_0,esk13_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[164,157,theory(equality)]),156,theory(equality)]) ).

cnf(166,negated_conjecture,
    ~ segmentP(esk14_0,esk13_0),
    inference(cn,[status(thm)],[165,theory(equality)]) ).

cnf(253,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[87,54,theory(equality)]) ).

cnf(259,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[253,115,theory(equality)]) ).

cnf(260,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[259,theory(equality)]) ).

cnf(2091,negated_conjecture,
    ( segmentP(X1,esk13_0)
    | esk14_0 != X1
    | ~ ssList(esk15_0)
    | ~ ssList(esk13_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[260,160,theory(equality)]) ).

cnf(2105,negated_conjecture,
    ( segmentP(X1,esk13_0)
    | esk14_0 != X1
    | ~ ssList(esk15_0)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[2091,162,theory(equality)]) ).

cnf(2106,negated_conjecture,
    ( segmentP(X1,esk13_0)
    | esk14_0 != X1
    | ~ ssList(esk15_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2105,theory(equality)]) ).

cnf(2300,negated_conjecture,
    ( segmentP(X1,esk13_0)
    | esk14_0 != X1
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[2106,158,theory(equality)]) ).

cnf(2435,negated_conjecture,
    ( segmentP(esk14_0,esk13_0)
    | ~ ssList(esk14_0) ),
    inference(er,[status(thm)],[2300,theory(equality)]) ).

cnf(2436,negated_conjecture,
    ( segmentP(esk14_0,esk13_0)
    | $false ),
    inference(rw,[status(thm)],[2435,163,theory(equality)]) ).

cnf(2437,negated_conjecture,
    segmentP(esk14_0,esk13_0),
    inference(cn,[status(thm)],[2436,theory(equality)]) ).

cnf(2438,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[2437,166,theory(equality)]) ).

cnf(2439,negated_conjecture,
    $false,
    2438,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC331+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp6GV9I6/sel_SWC331+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC331+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC331+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC331+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
% 
%------------------------------------------------------------------------------