TSTP Solution File: SWV403+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWV403+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 12:38:59 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   69 (  11 unt;   0 def)
%            Number of atoms       :  202 (  45 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  217 (  84   ~;  88   |;  34   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  148 (   7 sgn  88   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1,X2,X3,X4] :
      ( less_than(X3,X4)
     => update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
    file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',ax30) ).

fof(4,axiom,
    ! [X1,X2,X3,X4] :
      ( strictly_less_than(X4,X3)
     => update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
    file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',ax29) ).

fof(6,axiom,
    ! [X1,X2] :
      ( less_than(X1,X2)
      | less_than(X2,X1) ),
    file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',totality) ).

fof(7,axiom,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',stricly_smaller_definition) ).

fof(10,axiom,
    ! [X1,X2,X3,X4,X5] :
      ( pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
    <=> ( pair_in_list(X1,X3,X5)
        | ( X2 = X3
          & X4 = X5 ) ) ),
    file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',ax23) ).

fof(12,conjecture,
    ! [X1] :
      ( ! [X2,X3,X4] :
          ( ( pair_in_list(X1,X2,X3)
            & strictly_less_than(X3,X4) )
         => pair_in_list(update_slb(X1,X4),X2,X4) )
     => ! [X5,X6,X7,X8,X9] :
          ( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
            & strictly_less_than(X6,X7) )
         => pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
    file('/tmp/tmpop_l-_/sel_SWV403+1.p_1',l39_co) ).

fof(13,negated_conjecture,
    ~ ! [X1] :
        ( ! [X2,X3,X4] :
            ( ( pair_in_list(X1,X2,X3)
              & strictly_less_than(X3,X4) )
           => pair_in_list(update_slb(X1,X4),X2,X4) )
       => ! [X5,X6,X7,X8,X9] :
            ( ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
              & strictly_less_than(X6,X7) )
           => pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
    inference(assume_negation,[status(cth)],[12]) ).

fof(14,plain,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(22,plain,
    ! [X1,X2,X3,X4] :
      ( ~ less_than(X3,X4)
      | update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(23,plain,
    ! [X5,X6,X7,X8] :
      ( ~ less_than(X7,X8)
      | update_slb(insert_slb(X5,pair(X6,X8)),X7) = insert_slb(update_slb(X5,X7),pair(X6,X8)) ),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(24,plain,
    ( update_slb(insert_slb(X1,pair(X2,X3)),X4) = insert_slb(update_slb(X1,X4),pair(X2,X3))
    | ~ less_than(X4,X3) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(25,plain,
    ! [X1,X2,X3,X4] :
      ( ~ strictly_less_than(X4,X3)
      | update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(26,plain,
    ! [X5,X6,X7,X8] :
      ( ~ strictly_less_than(X8,X7)
      | update_slb(insert_slb(X5,pair(X6,X8)),X7) = insert_slb(update_slb(X5,X7),pair(X6,X7)) ),
    inference(variable_rename,[status(thm)],[25]) ).

cnf(27,plain,
    ( update_slb(insert_slb(X1,pair(X2,X3)),X4) = insert_slb(update_slb(X1,X4),pair(X2,X4))
    | ~ strictly_less_than(X3,X4) ),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(30,plain,
    ! [X3,X4] :
      ( less_than(X3,X4)
      | less_than(X4,X3) ),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(31,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(32,plain,
    ! [X1,X2] :
      ( ( ~ strictly_less_than(X1,X2)
        | ( less_than(X1,X2)
          & ~ less_than(X2,X1) ) )
      & ( ~ less_than(X1,X2)
        | less_than(X2,X1)
        | strictly_less_than(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(33,plain,
    ! [X3,X4] :
      ( ( ~ strictly_less_than(X3,X4)
        | ( less_than(X3,X4)
          & ~ less_than(X4,X3) ) )
      & ( ~ less_than(X3,X4)
        | less_than(X4,X3)
        | strictly_less_than(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[32]) ).

fof(34,plain,
    ! [X3,X4] :
      ( ( less_than(X3,X4)
        | ~ strictly_less_than(X3,X4) )
      & ( ~ less_than(X4,X3)
        | ~ strictly_less_than(X3,X4) )
      & ( ~ less_than(X3,X4)
        | less_than(X4,X3)
        | strictly_less_than(X3,X4) ) ),
    inference(distribute,[status(thm)],[33]) ).

cnf(35,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(36,plain,
    ( ~ strictly_less_than(X1,X2)
    | ~ less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(46,plain,
    ! [X1,X2,X3,X4,X5] :
      ( ( ~ pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
        | pair_in_list(X1,X3,X5)
        | ( X2 = X3
          & X4 = X5 ) )
      & ( ( ~ pair_in_list(X1,X3,X5)
          & ( X2 != X3
            | X4 != X5 ) )
        | pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(47,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( ~ pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10)
        | pair_in_list(X6,X8,X10)
        | ( X7 = X8
          & X9 = X10 ) )
      & ( ( ~ pair_in_list(X6,X8,X10)
          & ( X7 != X8
            | X9 != X10 ) )
        | pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) ) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,plain,
    ! [X6,X7,X8,X9,X10] :
      ( ( X7 = X8
        | pair_in_list(X6,X8,X10)
        | ~ pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) )
      & ( X9 = X10
        | pair_in_list(X6,X8,X10)
        | ~ pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) )
      & ( ~ pair_in_list(X6,X8,X10)
        | pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) )
      & ( X7 != X8
        | X9 != X10
        | pair_in_list(insert_slb(X6,pair(X7,X9)),X8,X10) ) ),
    inference(distribute,[status(thm)],[47]) ).

cnf(49,plain,
    ( pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5)
    | X3 != X5
    | X2 != X4 ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,plain,
    ( pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5)
    | ~ pair_in_list(X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(51,plain,
    ( pair_in_list(X1,X4,X5)
    | X3 = X5
    | ~ pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(52,plain,
    ( pair_in_list(X1,X4,X5)
    | X2 = X4
    | ~ pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X5) ),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(55,negated_conjecture,
    ? [X1] :
      ( ! [X2,X3,X4] :
          ( ~ pair_in_list(X1,X2,X3)
          | ~ strictly_less_than(X3,X4)
          | pair_in_list(update_slb(X1,X4),X2,X4) )
      & ? [X5,X6,X7,X8,X9] :
          ( pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6)
          & strictly_less_than(X6,X7)
          & ~ pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(56,negated_conjecture,
    ? [X10] :
      ( ! [X11,X12,X13] :
          ( ~ pair_in_list(X10,X11,X12)
          | ~ strictly_less_than(X12,X13)
          | pair_in_list(update_slb(X10,X13),X11,X13) )
      & ? [X14,X15,X16,X17,X18] :
          ( pair_in_list(insert_slb(X10,pair(X17,X18)),X14,X15)
          & strictly_less_than(X15,X16)
          & ~ pair_in_list(update_slb(insert_slb(X10,pair(X17,X18)),X16),X14,X16) ) ),
    inference(variable_rename,[status(thm)],[55]) ).

fof(57,negated_conjecture,
    ( ! [X11,X12,X13] :
        ( ~ pair_in_list(esk1_0,X11,X12)
        | ~ strictly_less_than(X12,X13)
        | pair_in_list(update_slb(esk1_0,X13),X11,X13) )
    & pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0)
    & strictly_less_than(esk3_0,esk4_0)
    & ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0) ),
    inference(skolemize,[status(esa)],[56]) ).

fof(58,negated_conjecture,
    ! [X11,X12,X13] :
      ( ( ~ pair_in_list(esk1_0,X11,X12)
        | ~ strictly_less_than(X12,X13)
        | pair_in_list(update_slb(esk1_0,X13),X11,X13) )
      & pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0)
      & strictly_less_than(esk3_0,esk4_0)
      & ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0) ),
    inference(shift_quantors,[status(thm)],[57]) ).

cnf(59,negated_conjecture,
    ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(60,negated_conjecture,
    strictly_less_than(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(61,negated_conjecture,
    pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(62,negated_conjecture,
    ( pair_in_list(update_slb(esk1_0,X1),X2,X1)
    | ~ strictly_less_than(X3,X1)
    | ~ pair_in_list(esk1_0,X2,X3) ),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(68,negated_conjecture,
    ~ less_than(esk4_0,esk3_0),
    inference(spm,[status(thm)],[36,60,theory(equality)]) ).

cnf(69,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[35,31]) ).

cnf(76,plain,
    ( pair_in_list(insert_slb(X1,pair(X2,X3)),X4,X3)
    | X2 != X4 ),
    inference(er,[status(thm)],[49,theory(equality)]) ).

cnf(77,plain,
    pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
    inference(er,[status(thm)],[76,theory(equality)]) ).

cnf(79,negated_conjecture,
    ( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk6_0)),esk2_0,esk4_0)
    | ~ less_than(esk4_0,esk6_0) ),
    inference(spm,[status(thm)],[59,24,theory(equality)]) ).

cnf(80,negated_conjecture,
    ( esk6_0 = esk3_0
    | pair_in_list(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[51,61,theory(equality)]) ).

cnf(82,negated_conjecture,
    ( esk5_0 = esk2_0
    | pair_in_list(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[52,61,theory(equality)]) ).

cnf(85,negated_conjecture,
    ( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk2_0,esk4_0)
    | ~ strictly_less_than(esk6_0,esk4_0) ),
    inference(spm,[status(thm)],[59,27,theory(equality)]) ).

cnf(100,negated_conjecture,
    ( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
    | esk6_0 = esk3_0
    | ~ strictly_less_than(esk3_0,X1) ),
    inference(spm,[status(thm)],[62,80,theory(equality)]) ).

cnf(101,negated_conjecture,
    ( pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
    | esk2_0 = esk5_0
    | ~ strictly_less_than(esk3_0,X1) ),
    inference(spm,[status(thm)],[62,82,theory(equality)]) ).

cnf(118,negated_conjecture,
    ( ~ strictly_less_than(esk6_0,esk4_0)
    | ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[85,50,theory(equality)]) ).

cnf(119,negated_conjecture,
    ( esk6_0 = esk3_0
    | ~ strictly_less_than(esk6_0,esk4_0)
    | ~ strictly_less_than(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[118,100,theory(equality)]) ).

cnf(120,negated_conjecture,
    ( esk2_0 = esk5_0
    | ~ strictly_less_than(esk6_0,esk4_0)
    | ~ strictly_less_than(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[118,101,theory(equality)]) ).

cnf(121,negated_conjecture,
    ( esk6_0 = esk3_0
    | ~ strictly_less_than(esk6_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[119,60,theory(equality)]) ).

cnf(122,negated_conjecture,
    ( esk6_0 = esk3_0
    | ~ strictly_less_than(esk6_0,esk4_0) ),
    inference(cn,[status(thm)],[121,theory(equality)]) ).

cnf(123,negated_conjecture,
    ( esk2_0 = esk5_0
    | ~ strictly_less_than(esk6_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[120,60,theory(equality)]) ).

cnf(124,negated_conjecture,
    ( esk2_0 = esk5_0
    | ~ strictly_less_than(esk6_0,esk4_0) ),
    inference(cn,[status(thm)],[123,theory(equality)]) ).

cnf(125,negated_conjecture,
    ( esk6_0 = esk3_0
    | less_than(esk4_0,esk6_0) ),
    inference(spm,[status(thm)],[122,69,theory(equality)]) ).

cnf(126,negated_conjecture,
    ( esk2_0 = esk5_0
    | less_than(esk4_0,esk6_0) ),
    inference(spm,[status(thm)],[124,69,theory(equality)]) ).

cnf(143,negated_conjecture,
    ( ~ less_than(esk4_0,esk6_0)
    | ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[79,50,theory(equality)]) ).

cnf(144,negated_conjecture,
    ( esk6_0 = esk3_0
    | ~ less_than(esk4_0,esk6_0)
    | ~ strictly_less_than(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[143,100,theory(equality)]) ).

cnf(146,negated_conjecture,
    ( esk6_0 = esk3_0
    | ~ less_than(esk4_0,esk6_0)
    | $false ),
    inference(rw,[status(thm)],[144,60,theory(equality)]) ).

cnf(147,negated_conjecture,
    ( esk6_0 = esk3_0
    | ~ less_than(esk4_0,esk6_0) ),
    inference(cn,[status(thm)],[146,theory(equality)]) ).

cnf(150,negated_conjecture,
    esk6_0 = esk3_0,
    inference(csr,[status(thm)],[147,125]) ).

cnf(152,negated_conjecture,
    ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk3_0)),esk4_0),esk2_0,esk4_0),
    inference(rw,[status(thm)],[59,150,theory(equality)]) ).

cnf(162,negated_conjecture,
    ( esk2_0 = esk5_0
    | less_than(esk4_0,esk3_0) ),
    inference(rw,[status(thm)],[126,150,theory(equality)]) ).

cnf(163,negated_conjecture,
    esk2_0 = esk5_0,
    inference(sr,[status(thm)],[162,68,theory(equality)]) ).

cnf(186,negated_conjecture,
    ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk3_0)),esk4_0),esk5_0,esk4_0),
    inference(rw,[status(thm)],[152,163,theory(equality)]) ).

cnf(188,negated_conjecture,
    ( ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk5_0,esk4_0)
    | ~ strictly_less_than(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[186,27,theory(equality)]) ).

cnf(189,negated_conjecture,
    ( $false
    | ~ strictly_less_than(esk3_0,esk4_0) ),
    inference(rw,[status(thm)],[188,77,theory(equality)]) ).

cnf(190,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[189,60,theory(equality)]) ).

cnf(191,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[190,theory(equality)]) ).

cnf(192,negated_conjecture,
    $false,
    191,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWV/SWV403+1.p
% --creating new selector for [SWV007+0.ax, SWV007+2.ax]
% -running prover on /tmp/tmpop_l-_/sel_SWV403+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWV403+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWV/SWV403+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWV/SWV403+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
% 
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