%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWV412+1 : TPTP v5.0.0. Released v3.3.0.
% 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 12:40:20 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   17 (   7 unt;   0 def)
%            Number of atoms       :   41 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   37 (  13   ~;   7   |;  14   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   33 (   0 sgn  20   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(12,axiom,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & strictly_less_than(X3,X4) )
     => pair_in_list(update_slb(X1,X4),X2,X4) ),
    file('/tmp/tmpKB_ZN6/sel_SWV412+1.p_1',l48_li3839) ).

fof(13,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( pair_in_list(X1,X2,X3)
        & strictly_less_than(X2,X4)
        & strictly_less_than(X3,X4) )
     => pair_in_list(update_slb(X1,X4),X2,X4) ),
    file('/tmp/tmpKB_ZN6/sel_SWV412+1.p_1',l48_co) ).

fof(14,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( pair_in_list(X1,X2,X3)
          & strictly_less_than(X2,X4)
          & strictly_less_than(X3,X4) )
       => pair_in_list(update_slb(X1,X4),X2,X4) ),
    inference(assume_negation,[status(cth)],[13]) ).

fof(56,plain,
    ! [X1,X2,X3,X4] :
      ( ~ pair_in_list(X1,X2,X3)
      | ~ strictly_less_than(X3,X4)
      | pair_in_list(update_slb(X1,X4),X2,X4) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(57,plain,
    ! [X5,X6,X7,X8] :
      ( ~ pair_in_list(X5,X6,X7)
      | ~ strictly_less_than(X7,X8)
      | pair_in_list(update_slb(X5,X8),X6,X8) ),
    inference(variable_rename,[status(thm)],[56]) ).

cnf(58,plain,
    ( pair_in_list(update_slb(X1,X2),X3,X2)
    | ~ strictly_less_than(X4,X2)
    | ~ pair_in_list(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[57]) ).

fof(59,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( pair_in_list(X1,X2,X3)
      & strictly_less_than(X2,X4)
      & strictly_less_than(X3,X4)
      & ~ pair_in_list(update_slb(X1,X4),X2,X4) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(60,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( pair_in_list(X5,X6,X7)
      & strictly_less_than(X6,X8)
      & strictly_less_than(X7,X8)
      & ~ pair_in_list(update_slb(X5,X8),X6,X8) ),
    inference(variable_rename,[status(thm)],[59]) ).

fof(61,negated_conjecture,
    ( pair_in_list(esk1_0,esk2_0,esk3_0)
    & strictly_less_than(esk2_0,esk4_0)
    & strictly_less_than(esk3_0,esk4_0)
    & ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
    inference(skolemize,[status(esa)],[60]) ).

cnf(62,negated_conjecture,
    ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(63,negated_conjecture,
    strictly_less_than(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(65,negated_conjecture,
    pair_in_list(esk1_0,esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[61]) ).

cnf(77,negated_conjecture,
    ( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
    | ~ strictly_less_than(esk3_0,X1) ),
    inference(spm,[status(thm)],[58,65,theory(equality)]) ).

cnf(104,negated_conjecture,
    ~ strictly_less_than(esk3_0,esk4_0),
    inference(spm,[status(thm)],[62,77,theory(equality)]) ).

cnf(106,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[104,63,theory(equality)]) ).

cnf(107,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[106,theory(equality)]) ).

cnf(108,negated_conjecture,
    $false,
    107,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV412+1.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax]
% -running prover on /tmp/tmpKB_ZN6/sel_SWV412+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV412+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV412+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV412+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
% 
%------------------------------------------------------------------------------