TSTP Solution File: SWC277+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC277+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 11:11:26 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   76 (  18 unt;   0 def)
%            Number of atoms       :  296 (  63 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  364 ( 144   ~; 150   |;  46   &)
%                                         (   3 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   79 (   0 sgn  52   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( ssItem(X1)
     => totalorderedP(cons(X1,nil)) ),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',ax65) ).

fof(3,axiom,
    totalorderedP(nil),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',ax66) ).

fof(21,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( singletonP(X1)
      <=> ? [X2] :
            ( ssItem(X2)
            & cons(X2,nil) = X1 ) ) ),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',ax4) ).

fof(26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( segmentP(nil,X1)
      <=> nil = X1 ) ),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',ax58) ).

fof(27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',ax15) ).

fof(29,axiom,
    ssList(nil),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',ax17) ).

fof(31,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( ( segmentP(X1,X2)
                  & segmentP(X2,X3) )
               => segmentP(X1,X3) ) ) ) ),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',ax53) ).

fof(39,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ segmentP(X4,X3)
                    | totalorderedP(X1)
                    | ( ~ singletonP(X3)
                      & neq(X4,nil) ) ) ) ) ) ),
    file('/tmp/tmpl-tZy0/sel_SWC277+1.p_1',co1) ).

fof(40,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ segmentP(X4,X3)
                      | totalorderedP(X1)
                      | ( ~ singletonP(X3)
                        & neq(X4,nil) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[39]) ).

fof(42,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ segmentP(X4,X3)
                      | totalorderedP(X1)
                      | ( ~ singletonP(X3)
                        & neq(X4,nil) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[40,theory(equality)]) ).

fof(43,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | totalorderedP(cons(X1,nil)) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(44,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | totalorderedP(cons(X2,nil)) ),
    inference(variable_rename,[status(thm)],[43]) ).

cnf(45,plain,
    ( totalorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(55,plain,
    totalorderedP(nil),
    inference(split_conjunct,[status(thm)],[3]) ).

fof(130,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ( ( ~ singletonP(X1)
          | ? [X2] :
              ( ssItem(X2)
              & cons(X2,nil) = X1 ) )
        & ( ! [X2] :
              ( ~ ssItem(X2)
              | cons(X2,nil) != X1 )
          | singletonP(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(131,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ( ( ~ singletonP(X3)
          | ? [X4] :
              ( ssItem(X4)
              & cons(X4,nil) = X3 ) )
        & ( ! [X5] :
              ( ~ ssItem(X5)
              | cons(X5,nil) != X3 )
          | singletonP(X3) ) ) ),
    inference(variable_rename,[status(thm)],[130]) ).

fof(132,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ( ( ~ singletonP(X3)
          | ( ssItem(esk7_1(X3))
            & cons(esk7_1(X3),nil) = X3 ) )
        & ( ! [X5] :
              ( ~ ssItem(X5)
              | cons(X5,nil) != X3 )
          | singletonP(X3) ) ) ),
    inference(skolemize,[status(esa)],[131]) ).

fof(133,plain,
    ! [X3,X5] :
      ( ( ( ~ ssItem(X5)
          | cons(X5,nil) != X3
          | singletonP(X3) )
        & ( ~ singletonP(X3)
          | ( ssItem(esk7_1(X3))
            & cons(esk7_1(X3),nil) = X3 ) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[132]) ).

fof(134,plain,
    ! [X3,X5] :
      ( ( ~ ssItem(X5)
        | cons(X5,nil) != X3
        | singletonP(X3)
        | ~ ssList(X3) )
      & ( ssItem(esk7_1(X3))
        | ~ singletonP(X3)
        | ~ ssList(X3) )
      & ( cons(esk7_1(X3),nil) = X3
        | ~ singletonP(X3)
        | ~ ssList(X3) ) ),
    inference(distribute,[status(thm)],[133]) ).

cnf(135,plain,
    ( cons(esk7_1(X1),nil) = X1
    | ~ ssList(X1)
    | ~ singletonP(X1) ),
    inference(split_conjunct,[status(thm)],[134]) ).

cnf(136,plain,
    ( ssItem(esk7_1(X1))
    | ~ ssList(X1)
    | ~ singletonP(X1) ),
    inference(split_conjunct,[status(thm)],[134]) ).

fof(158,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ( ( ~ segmentP(nil,X1)
          | nil = X1 )
        & ( nil != X1
          | segmentP(nil,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(159,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | ( ( ~ segmentP(nil,X2)
          | nil = X2 )
        & ( nil != X2
          | segmentP(nil,X2) ) ) ),
    inference(variable_rename,[status(thm)],[158]) ).

fof(160,plain,
    ! [X2] :
      ( ( ~ segmentP(nil,X2)
        | nil = X2
        | ~ ssList(X2) )
      & ( nil != X2
        | segmentP(nil,X2)
        | ~ ssList(X2) ) ),
    inference(distribute,[status(thm)],[159]) ).

cnf(161,plain,
    ( segmentP(nil,X1)
    | ~ ssList(X1)
    | nil != X1 ),
    inference(split_conjunct,[status(thm)],[160]) ).

cnf(162,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ segmentP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[160]) ).

fof(163,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(164,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[163]) ).

fof(165,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[164]) ).

fof(166,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)],[165]) ).

cnf(167,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[166]) ).

cnf(173,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(187,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X2,X3)
              | segmentP(X1,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(188,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | ~ segmentP(X4,X5)
              | ~ segmentP(X5,X6)
              | segmentP(X4,X6) ) ) ),
    inference(variable_rename,[status(thm)],[187]) ).

fof(189,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | ~ segmentP(X4,X5)
      | ~ segmentP(X5,X6)
      | segmentP(X4,X6)
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[188]) ).

cnf(190,plain,
    ( segmentP(X1,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ segmentP(X2,X3)
    | ~ segmentP(X1,X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[189]) ).

fof(218,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & segmentP(X4,X3)
                  & ~ totalorderedP(X1)
                  & ( singletonP(X3)
                    | ~ neq(X4,nil) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(219,negated_conjecture,
    ? [X5] :
      ( ssList(X5)
      & ? [X6] :
          ( ssList(X6)
          & ? [X7] :
              ( ssList(X7)
              & ? [X8] :
                  ( ssList(X8)
                  & X6 = X8
                  & X5 = X7
                  & segmentP(X8,X7)
                  & ~ totalorderedP(X5)
                  & ( singletonP(X7)
                    | ~ neq(X8,nil) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[218]) ).

fof(220,negated_conjecture,
    ( ssList(esk14_0)
    & ssList(esk15_0)
    & ssList(esk16_0)
    & ssList(esk17_0)
    & esk15_0 = esk17_0
    & esk14_0 = esk16_0
    & segmentP(esk17_0,esk16_0)
    & ~ totalorderedP(esk14_0)
    & ( singletonP(esk16_0)
      | ~ neq(esk17_0,nil) ) ),
    inference(skolemize,[status(esa)],[219]) ).

cnf(221,negated_conjecture,
    ( singletonP(esk16_0)
    | ~ neq(esk17_0,nil) ),
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(222,negated_conjecture,
    ~ totalorderedP(esk14_0),
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(223,negated_conjecture,
    segmentP(esk17_0,esk16_0),
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(224,negated_conjecture,
    esk14_0 = esk16_0,
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(225,negated_conjecture,
    esk15_0 = esk17_0,
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(228,negated_conjecture,
    ssList(esk15_0),
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(229,negated_conjecture,
    ssList(esk14_0),
    inference(split_conjunct,[status(thm)],[220]) ).

cnf(230,negated_conjecture,
    ssList(esk16_0),
    inference(rw,[status(thm)],[229,224,theory(equality)]) ).

cnf(231,negated_conjecture,
    ssList(esk17_0),
    inference(rw,[status(thm)],[228,225,theory(equality)]) ).

cnf(232,negated_conjecture,
    ~ totalorderedP(esk16_0),
    inference(rw,[status(thm)],[222,224,theory(equality)]) ).

cnf(234,negated_conjecture,
    ( singletonP(esk16_0)
    | esk17_0 = nil
    | ~ ssList(nil)
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[221,167,theory(equality)]) ).

cnf(235,negated_conjecture,
    ( singletonP(esk16_0)
    | esk17_0 = nil
    | $false
    | ~ ssList(esk17_0) ),
    inference(rw,[status(thm)],[234,173,theory(equality)]) ).

cnf(236,negated_conjecture,
    ( singletonP(esk16_0)
    | esk17_0 = nil
    | ~ ssList(esk17_0) ),
    inference(cn,[status(thm)],[235,theory(equality)]) ).

cnf(259,plain,
    ( totalorderedP(X1)
    | ~ ssItem(esk7_1(X1))
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[45,135,theory(equality)]) ).

cnf(270,negated_conjecture,
    ( segmentP(X1,esk16_0)
    | ~ segmentP(X1,esk17_0)
    | ~ ssList(esk16_0)
    | ~ ssList(esk17_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[190,223,theory(equality)]) ).

cnf(515,negated_conjecture,
    ( singletonP(esk16_0)
    | esk17_0 = nil
    | $false ),
    inference(rw,[status(thm)],[236,231,theory(equality)]) ).

cnf(516,negated_conjecture,
    ( singletonP(esk16_0)
    | esk17_0 = nil ),
    inference(cn,[status(thm)],[515,theory(equality)]) ).

cnf(539,negated_conjecture,
    ( segmentP(X1,esk16_0)
    | ~ segmentP(X1,esk17_0)
    | $false
    | ~ ssList(esk17_0)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[270,230,theory(equality)]) ).

cnf(540,negated_conjecture,
    ( segmentP(X1,esk16_0)
    | ~ segmentP(X1,esk17_0)
    | $false
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[539,231,theory(equality)]) ).

cnf(541,negated_conjecture,
    ( segmentP(X1,esk16_0)
    | ~ segmentP(X1,esk17_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[540,theory(equality)]) ).

cnf(542,negated_conjecture,
    ( nil = esk16_0
    | ~ ssList(esk16_0)
    | ~ segmentP(nil,esk17_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[162,541,theory(equality)]) ).

cnf(545,negated_conjecture,
    ( nil = esk16_0
    | $false
    | ~ segmentP(nil,esk17_0)
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[542,230,theory(equality)]) ).

cnf(546,negated_conjecture,
    ( nil = esk16_0
    | $false
    | ~ segmentP(nil,esk17_0)
    | $false ),
    inference(rw,[status(thm)],[545,173,theory(equality)]) ).

cnf(547,negated_conjecture,
    ( nil = esk16_0
    | ~ segmentP(nil,esk17_0) ),
    inference(cn,[status(thm)],[546,theory(equality)]) ).

cnf(552,negated_conjecture,
    ( esk16_0 = nil
    | nil != esk17_0
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[547,161,theory(equality)]) ).

cnf(553,negated_conjecture,
    ( esk16_0 = nil
    | nil != esk17_0
    | $false ),
    inference(rw,[status(thm)],[552,231,theory(equality)]) ).

cnf(554,negated_conjecture,
    ( esk16_0 = nil
    | nil != esk17_0 ),
    inference(cn,[status(thm)],[553,theory(equality)]) ).

cnf(572,negated_conjecture,
    ( ~ totalorderedP(nil)
    | esk17_0 != nil ),
    inference(spm,[status(thm)],[232,554,theory(equality)]) ).

cnf(578,negated_conjecture,
    ( $false
    | esk17_0 != nil ),
    inference(rw,[status(thm)],[572,55,theory(equality)]) ).

cnf(579,negated_conjecture,
    esk17_0 != nil,
    inference(cn,[status(thm)],[578,theory(equality)]) ).

cnf(590,negated_conjecture,
    singletonP(esk16_0),
    inference(sr,[status(thm)],[516,579,theory(equality)]) ).

cnf(613,plain,
    ( totalorderedP(X1)
    | ~ singletonP(X1)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[259,136]) ).

cnf(614,negated_conjecture,
    ( totalorderedP(esk16_0)
    | ~ ssList(esk16_0) ),
    inference(spm,[status(thm)],[613,590,theory(equality)]) ).

cnf(615,negated_conjecture,
    ( totalorderedP(esk16_0)
    | $false ),
    inference(rw,[status(thm)],[614,230,theory(equality)]) ).

cnf(616,negated_conjecture,
    totalorderedP(esk16_0),
    inference(cn,[status(thm)],[615,theory(equality)]) ).

cnf(617,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[616,232,theory(equality)]) ).

cnf(618,negated_conjecture,
    $false,
    617,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC277+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpl-tZy0/sel_SWC277+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC277+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC277+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC277+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
% 
%------------------------------------------------------------------------------