TSTP Solution File: SWC243+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC243+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 11:04:01 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   58 (   7 unt;   0 def)
%            Number of atoms       :  311 (  82 equ)
%            Maximal formula atoms :   33 (   5 avg)
%            Number of connectives :  414 ( 161   ~; 148   |;  82   &)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :  123 (   0 sgn  58   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax81) ).

fof(11,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax28) ).

fof(15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax20) ).

fof(27,axiom,
    ssList(nil),
    file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax17) ).

fof(31,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax38) ).

fof(35,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',ax16) ).

fof(38,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ totalorderedP(X3)
                    | nil = X1
                    | ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & app(app(X6,cons(X5,nil)),X7) = X1
                                & ! [X8] :
                                    ( ssItem(X8)
                                   => ( ~ memberP(X6,X8)
                                      | ~ memberP(X7,X8)
                                      | ~ lt(X5,X8)
                                      | leq(X5,X8) ) ) ) ) ) ) ) ) ) ),
    file('/tmp/tmp_gn9gL/sel_SWC243+1.p_1',co1) ).

fof(39,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ totalorderedP(X3)
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X1
                                  & ! [X8] :
                                      ( ssItem(X8)
                                     => ( ~ memberP(X6,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ lt(X5,X8)
                                        | leq(X5,X8) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[38]) ).

fof(42,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).

fof(43,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ totalorderedP(X3)
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X1
                                  & ! [X8] :
                                      ( ssItem(X8)
                                     => ( ~ memberP(X6,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ lt(X5,X8)
                                        | leq(X5,X8) ) ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[39,theory(equality)]) ).

fof(75,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(76,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) = app(cons(X4,nil),X3) ) ),
    inference(variable_rename,[status(thm)],[75]) ).

fof(77,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) = app(cons(X4,nil),X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[76]) ).

cnf(78,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[77]) ).

fof(87,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(88,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[87]) ).

cnf(89,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[88]) ).

fof(102,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssItem(X3)
              & cons(X3,X2) = X1 ) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(103,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ? [X5] :
          ( ssList(X5)
          & ? [X6] :
              ( ssItem(X6)
              & cons(X6,X5) = X4 ) ) ),
    inference(variable_rename,[status(thm)],[102]) ).

fof(104,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ( ssList(esk1_1(X4))
        & ssItem(esk2_1(X4))
        & cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
    inference(skolemize,[status(esa)],[103]) ).

fof(105,plain,
    ! [X4] :
      ( ( ssList(esk1_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( ssItem(esk2_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( cons(esk2_1(X4),esk1_1(X4)) = X4
        | nil = X4
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[104]) ).

cnf(106,plain,
    ( nil = X1
    | cons(esk2_1(X1),esk1_1(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(107,plain,
    ( nil = X1
    | ssItem(esk2_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(108,plain,
    ( nil = X1
    | ssList(esk1_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

cnf(159,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(184,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ memberP(nil,X1) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(185,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | ~ memberP(nil,X2) ),
    inference(variable_rename,[status(thm)],[184]) ).

cnf(186,plain,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[185]) ).

fof(204,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(205,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[204]) ).

fof(206,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[205]) ).

cnf(207,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[206]) ).

fof(218,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & totalorderedP(X3)
                  & nil != X1
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(app(X6,cons(X5,nil)),X7) != X1
                              | ? [X8] :
                                  ( ssItem(X8)
                                  & memberP(X6,X8)
                                  & memberP(X7,X8)
                                  & lt(X5,X8)
                                  & ~ leq(X5,X8) ) ) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[43]) ).

fof(219,negated_conjecture,
    ? [X9] :
      ( ssList(X9)
      & ? [X10] :
          ( ssList(X10)
          & ? [X11] :
              ( ssList(X11)
              & ? [X12] :
                  ( ssList(X12)
                  & X10 = X12
                  & X9 = X11
                  & totalorderedP(X11)
                  & nil != X9
                  & ! [X13] :
                      ( ~ ssItem(X13)
                      | ! [X14] :
                          ( ~ ssList(X14)
                          | ! [X15] :
                              ( ~ ssList(X15)
                              | app(app(X14,cons(X13,nil)),X15) != X9
                              | ? [X16] :
                                  ( ssItem(X16)
                                  & memberP(X14,X16)
                                  & memberP(X15,X16)
                                  & lt(X13,X16)
                                  & ~ leq(X13,X16) ) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[218]) ).

fof(220,negated_conjecture,
    ( ssList(esk13_0)
    & ssList(esk14_0)
    & ssList(esk15_0)
    & ssList(esk16_0)
    & esk14_0 = esk16_0
    & esk13_0 = esk15_0
    & totalorderedP(esk15_0)
    & nil != esk13_0
    & ! [X13] :
        ( ~ ssItem(X13)
        | ! [X14] :
            ( ~ ssList(X14)
            | ! [X15] :
                ( ~ ssList(X15)
                | app(app(X14,cons(X13,nil)),X15) != esk13_0
                | ( ssItem(esk17_3(X13,X14,X15))
                  & memberP(X14,esk17_3(X13,X14,X15))
                  & memberP(X15,esk17_3(X13,X14,X15))
                  & lt(X13,esk17_3(X13,X14,X15))
                  & ~ leq(X13,esk17_3(X13,X14,X15)) ) ) ) ) ),
    inference(skolemize,[status(esa)],[219]) ).

fof(221,negated_conjecture,
    ! [X13,X14,X15] :
      ( ( ~ ssList(X15)
        | app(app(X14,cons(X13,nil)),X15) != esk13_0
        | ( ssItem(esk17_3(X13,X14,X15))
          & memberP(X14,esk17_3(X13,X14,X15))
          & memberP(X15,esk17_3(X13,X14,X15))
          & lt(X13,esk17_3(X13,X14,X15))
          & ~ leq(X13,esk17_3(X13,X14,X15)) )
        | ~ ssList(X14)
        | ~ ssItem(X13) )
      & esk14_0 = esk16_0
      & esk13_0 = esk15_0
      & totalorderedP(esk15_0)
      & nil != esk13_0
      & ssList(esk16_0)
      & ssList(esk15_0)
      & ssList(esk14_0)
      & ssList(esk13_0) ),
    inference(shift_quantors,[status(thm)],[220]) ).

fof(222,negated_conjecture,
    ! [X13,X14,X15] :
      ( ( ssItem(esk17_3(X13,X14,X15))
        | ~ ssList(X15)
        | app(app(X14,cons(X13,nil)),X15) != esk13_0
        | ~ ssList(X14)
        | ~ ssItem(X13) )
      & ( memberP(X14,esk17_3(X13,X14,X15))
        | ~ ssList(X15)
        | app(app(X14,cons(X13,nil)),X15) != esk13_0
        | ~ ssList(X14)
        | ~ ssItem(X13) )
      & ( memberP(X15,esk17_3(X13,X14,X15))
        | ~ ssList(X15)
        | app(app(X14,cons(X13,nil)),X15) != esk13_0
        | ~ ssList(X14)
        | ~ ssItem(X13) )
      & ( lt(X13,esk17_3(X13,X14,X15))
        | ~ ssList(X15)
        | app(app(X14,cons(X13,nil)),X15) != esk13_0
        | ~ ssList(X14)
        | ~ ssItem(X13) )
      & ( ~ leq(X13,esk17_3(X13,X14,X15))
        | ~ ssList(X15)
        | app(app(X14,cons(X13,nil)),X15) != esk13_0
        | ~ ssList(X14)
        | ~ ssItem(X13) )
      & esk14_0 = esk16_0
      & esk13_0 = esk15_0
      & totalorderedP(esk15_0)
      & nil != esk13_0
      & ssList(esk16_0)
      & ssList(esk15_0)
      & ssList(esk14_0)
      & ssList(esk13_0) ),
    inference(distribute,[status(thm)],[221]) ).

cnf(223,negated_conjecture,
    ssList(esk13_0),
    inference(split_conjunct,[status(thm)],[222]) ).

cnf(227,negated_conjecture,
    nil != esk13_0,
    inference(split_conjunct,[status(thm)],[222]) ).

cnf(234,negated_conjecture,
    ( memberP(X2,esk17_3(X1,X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk13_0
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[222]) ).

cnf(235,negated_conjecture,
    ( ssItem(esk17_3(X1,X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk13_0
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[222]) ).

cnf(425,negated_conjecture,
    ( ~ ssItem(esk17_3(X1,nil,X2))
    | app(app(nil,cons(X1,nil)),X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssList(nil)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[186,234,theory(equality)]) ).

cnf(428,negated_conjecture,
    ( ~ ssItem(esk17_3(X1,nil,X2))
    | app(app(nil,cons(X1,nil)),X2) != esk13_0
    | ~ ssList(X2)
    | $false
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[425,159,theory(equality)]) ).

cnf(429,negated_conjecture,
    ( ~ ssItem(esk17_3(X1,nil,X2))
    | app(app(nil,cons(X1,nil)),X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[428,theory(equality)]) ).

cnf(1000,negated_conjecture,
    ( app(app(nil,cons(X1,nil)),X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[429,235,theory(equality)]) ).

cnf(1001,negated_conjecture,
    ( app(app(nil,cons(X1,nil)),X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[1000,159,theory(equality)]) ).

cnf(1002,negated_conjecture,
    ( app(app(nil,cons(X1,nil)),X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[1001,theory(equality)]) ).

cnf(1004,negated_conjecture,
    ( app(cons(X1,nil),X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[1002,89,theory(equality)]) ).

cnf(1103,negated_conjecture,
    ( cons(X1,X2) != esk13_0
    | ~ ssList(cons(X1,nil))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[1004,78,theory(equality)]) ).

cnf(1184,negated_conjecture,
    ( cons(X1,X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[1103,207,theory(equality)]) ).

cnf(1185,negated_conjecture,
    ( cons(X1,X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[1184,159,theory(equality)]) ).

cnf(1186,negated_conjecture,
    ( cons(X1,X2) != esk13_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[1185,theory(equality)]) ).

cnf(1207,negated_conjecture,
    ( nil = X1
    | X1 != esk13_0
    | ~ ssList(esk1_1(X1))
    | ~ ssItem(esk2_1(X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[1186,106,theory(equality)]) ).

cnf(1299,negated_conjecture,
    ( nil = X1
    | X1 != esk13_0
    | ~ ssList(esk1_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[1207,107]) ).

cnf(1300,negated_conjecture,
    ( nil = X1
    | X1 != esk13_0
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[1299,108]) ).

cnf(1301,negated_conjecture,
    nil = esk13_0,
    inference(spm,[status(thm)],[1300,223,theory(equality)]) ).

cnf(1311,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1301,227,theory(equality)]) ).

cnf(1312,negated_conjecture,
    $false,
    1311,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC243+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp_gn9gL/sel_SWC243+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC243+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC243+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC243+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
% 
%------------------------------------------------------------------------------