TSTP Solution File: SWW101+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWW101+1 : TPTP v5.2.0. Released v5.2.0.
% 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 : Mon Feb 28 18:32:46 EST 2011

% Result   : Theorem 0.90s
% Output   : CNFRefutation 0.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  121 (  35 unt;   0 def)
%            Number of atoms       :  391 ( 201 equ)
%            Maximal formula atoms :   75 (   3 avg)
%            Number of connectives :  409 ( 139   ~; 190   |;  72   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   73 (   4 sgn  43   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] : lazy_impl(false,X1) = true,
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',lazy_impl_axiom2) ).

fof(2,axiom,
    ! [X1] : lazy_impl(true,X1) = phi(X1),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',lazy_impl_axiom3) ).

fof(3,axiom,
    ! [X2,X1] :
      ( ~ bool(X2)
     => lazy_impl(X2,X1) = phi(X2) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',lazy_impl_axiom1) ).

fof(11,axiom,
    ! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',def_f7) ).

fof(12,axiom,
    ! [X3] :
      ( prop(X3) = false
    <=> ~ bool(X3) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',prop_false) ).

fof(13,axiom,
    ( d(true)
    & d(false)
    & d(err) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',false_true_err_in_d) ).

fof(14,axiom,
    ! [X3] :
      ( bool(X3)
    <=> ( X3 = false
        | X3 = true ) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',def_bool) ).

fof(19,axiom,
    ! [X3,X4] :
      ( forallprefers(X3,X4)
    <=> ( ( ~ d(X3)
          & d(X4) )
        | ( d(X3)
          & d(X4)
          & ~ bool(X3)
          & bool(X4) )
        | ( X3 = false
          & X4 = true ) ) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',def_forallprefers) ).

fof(20,axiom,
    ( true != false
    & true != err
    & false != err ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',distinct_false_true_err) ).

fof(21,axiom,
    false1 = false,
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',def_false1) ).

fof(22,axiom,
    ? [X5] :
      ( false2 = phi(f7(X5))
      & ~ ? [X9] : forallprefers(f7(X9),f7(X5)) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',def_false2) ).

fof(23,axiom,
    ! [X3] :
      ( prop(X3) = true
    <=> bool(X3) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',prop_true) ).

fof(24,axiom,
    ! [X3] :
      ( ( d(X3)
        & phi(X3) = X3 )
      | ( ~ d(X3)
        & phi(X3) = err ) ),
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',def_phi) ).

fof(25,conjecture,
    false1 = false2,
    file('/tmp/tmpigo5AL/sel_SWW101+1.p_5',false1_false2) ).

fof(26,negated_conjecture,
    false1 != false2,
    inference(assume_negation,[status(cth)],[25]) ).

fof(27,plain,
    ! [X2,X1] :
      ( ~ bool(X2)
     => lazy_impl(X2,X1) = phi(X2) ),
    inference(fof_simplification,[status(thm)],[3,theory(equality)]) ).

fof(29,plain,
    ! [X3] :
      ( prop(X3) = false
    <=> ~ bool(X3) ),
    inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).

fof(32,plain,
    ! [X3,X4] :
      ( forallprefers(X3,X4)
    <=> ( ( ~ d(X3)
          & d(X4) )
        | ( d(X3)
          & d(X4)
          & ~ bool(X3)
          & bool(X4) )
        | ( X3 = false
          & X4 = true ) ) ),
    inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).

fof(33,plain,
    ! [X3] :
      ( ( d(X3)
        & phi(X3) = X3 )
      | ( ~ d(X3)
        & phi(X3) = err ) ),
    inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).

fof(34,negated_conjecture,
    false1 != false2,
    inference(fof_simplification,[status(thm)],[26,theory(equality)]) ).

fof(35,plain,
    ! [X2] : lazy_impl(false,X2) = true,
    inference(variable_rename,[status(thm)],[1]) ).

cnf(36,plain,
    lazy_impl(false,X1) = true,
    inference(split_conjunct,[status(thm)],[35]) ).

fof(37,plain,
    ! [X2] : lazy_impl(true,X2) = phi(X2),
    inference(variable_rename,[status(thm)],[2]) ).

cnf(38,plain,
    lazy_impl(true,X1) = phi(X1),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(39,plain,
    ! [X2,X1] :
      ( bool(X2)
      | lazy_impl(X2,X1) = phi(X2) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(40,plain,
    ! [X3,X4] :
      ( bool(X3)
      | lazy_impl(X3,X4) = phi(X3) ),
    inference(variable_rename,[status(thm)],[39]) ).

cnf(41,plain,
    ( lazy_impl(X1,X2) = phi(X1)
    | bool(X1) ),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(88,plain,
    ! [X6] : f7(X6) = lazy_impl(prop(X6),X6),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(89,plain,
    f7(X1) = lazy_impl(prop(X1),X1),
    inference(split_conjunct,[status(thm)],[88]) ).

fof(90,plain,
    ! [X3] :
      ( ( prop(X3) != false
        | ~ bool(X3) )
      & ( bool(X3)
        | prop(X3) = false ) ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(91,plain,
    ! [X4] :
      ( ( prop(X4) != false
        | ~ bool(X4) )
      & ( bool(X4)
        | prop(X4) = false ) ),
    inference(variable_rename,[status(thm)],[90]) ).

cnf(92,plain,
    ( prop(X1) = false
    | bool(X1) ),
    inference(split_conjunct,[status(thm)],[91]) ).

cnf(95,plain,
    d(false),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(96,plain,
    d(true),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(97,plain,
    ! [X3] :
      ( ( ~ bool(X3)
        | X3 = false
        | X3 = true )
      & ( ( X3 != false
          & X3 != true )
        | bool(X3) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(98,plain,
    ! [X4] :
      ( ( ~ bool(X4)
        | X4 = false
        | X4 = true )
      & ( ( X4 != false
          & X4 != true )
        | bool(X4) ) ),
    inference(variable_rename,[status(thm)],[97]) ).

fof(99,plain,
    ! [X4] :
      ( ( ~ bool(X4)
        | X4 = false
        | X4 = true )
      & ( X4 != false
        | bool(X4) )
      & ( X4 != true
        | bool(X4) ) ),
    inference(distribute,[status(thm)],[98]) ).

cnf(100,plain,
    ( bool(X1)
    | X1 != true ),
    inference(split_conjunct,[status(thm)],[99]) ).

cnf(101,plain,
    ( bool(X1)
    | X1 != false ),
    inference(split_conjunct,[status(thm)],[99]) ).

cnf(102,plain,
    ( X1 = true
    | X1 = false
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[99]) ).

fof(115,plain,
    ! [X3,X4] :
      ( ( ~ forallprefers(X3,X4)
        | ( ~ d(X3)
          & d(X4) )
        | ( d(X3)
          & d(X4)
          & ~ bool(X3)
          & bool(X4) )
        | ( X3 = false
          & X4 = true ) )
      & ( ( ( d(X3)
            | ~ d(X4) )
          & ( ~ d(X3)
            | ~ d(X4)
            | bool(X3)
            | ~ bool(X4) )
          & ( X3 != false
            | X4 != true ) )
        | forallprefers(X3,X4) ) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(116,plain,
    ! [X5,X6] :
      ( ( ~ forallprefers(X5,X6)
        | ( ~ d(X5)
          & d(X6) )
        | ( d(X5)
          & d(X6)
          & ~ bool(X5)
          & bool(X6) )
        | ( X5 = false
          & X6 = true ) )
      & ( ( ( d(X5)
            | ~ d(X6) )
          & ( ~ d(X5)
            | ~ d(X6)
            | bool(X5)
            | ~ bool(X6) )
          & ( X5 != false
            | X6 != true ) )
        | forallprefers(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[115]) ).

fof(117,plain,
    ! [X5,X6] :
      ( ( X5 = false
        | d(X5)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | d(X5)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X5 = false
        | d(X6)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | d(X6)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X5 = false
        | ~ bool(X5)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | ~ bool(X5)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X5 = false
        | bool(X6)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | bool(X6)
        | ~ d(X5)
        | ~ forallprefers(X5,X6) )
      & ( X5 = false
        | d(X5)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | d(X5)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( X5 = false
        | d(X6)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | d(X6)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( X5 = false
        | ~ bool(X5)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | ~ bool(X5)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( X5 = false
        | bool(X6)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( X6 = true
        | bool(X6)
        | d(X6)
        | ~ forallprefers(X5,X6) )
      & ( d(X5)
        | ~ d(X6)
        | forallprefers(X5,X6) )
      & ( ~ d(X5)
        | ~ d(X6)
        | bool(X5)
        | ~ bool(X6)
        | forallprefers(X5,X6) )
      & ( X5 != false
        | X6 != true
        | forallprefers(X5,X6) ) ),
    inference(distribute,[status(thm)],[116]) ).

cnf(118,plain,
    ( forallprefers(X1,X2)
    | X2 != true
    | X1 != false ),
    inference(split_conjunct,[status(thm)],[117]) ).

cnf(137,plain,
    false != err,
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(138,plain,
    true != err,
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(139,plain,
    true != false,
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(140,plain,
    false1 = false,
    inference(split_conjunct,[status(thm)],[21]) ).

fof(141,plain,
    ? [X5] :
      ( false2 = phi(f7(X5))
      & ! [X9] : ~ forallprefers(f7(X9),f7(X5)) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(142,plain,
    ? [X10] :
      ( false2 = phi(f7(X10))
      & ! [X11] : ~ forallprefers(f7(X11),f7(X10)) ),
    inference(variable_rename,[status(thm)],[141]) ).

fof(143,plain,
    ( false2 = phi(f7(esk4_0))
    & ! [X11] : ~ forallprefers(f7(X11),f7(esk4_0)) ),
    inference(skolemize,[status(esa)],[142]) ).

fof(144,plain,
    ! [X11] :
      ( ~ forallprefers(f7(X11),f7(esk4_0))
      & false2 = phi(f7(esk4_0)) ),
    inference(shift_quantors,[status(thm)],[143]) ).

cnf(145,plain,
    false2 = phi(f7(esk4_0)),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(146,plain,
    ~ forallprefers(f7(X1),f7(esk4_0)),
    inference(split_conjunct,[status(thm)],[144]) ).

fof(147,plain,
    ! [X3] :
      ( ( prop(X3) != true
        | bool(X3) )
      & ( ~ bool(X3)
        | prop(X3) = true ) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(148,plain,
    ! [X4] :
      ( ( prop(X4) != true
        | bool(X4) )
      & ( ~ bool(X4)
        | prop(X4) = true ) ),
    inference(variable_rename,[status(thm)],[147]) ).

cnf(149,plain,
    ( prop(X1) = true
    | ~ bool(X1) ),
    inference(split_conjunct,[status(thm)],[148]) ).

fof(151,plain,
    ! [X4] :
      ( ( d(X4)
        & phi(X4) = X4 )
      | ( ~ d(X4)
        & phi(X4) = err ) ),
    inference(variable_rename,[status(thm)],[33]) ).

fof(152,plain,
    ! [X4] :
      ( ( ~ d(X4)
        | d(X4) )
      & ( phi(X4) = err
        | d(X4) )
      & ( ~ d(X4)
        | phi(X4) = X4 )
      & ( phi(X4) = err
        | phi(X4) = X4 ) ),
    inference(distribute,[status(thm)],[151]) ).

cnf(153,plain,
    ( phi(X1) = X1
    | phi(X1) = err ),
    inference(split_conjunct,[status(thm)],[152]) ).

cnf(154,plain,
    ( phi(X1) = X1
    | ~ d(X1) ),
    inference(split_conjunct,[status(thm)],[152]) ).

cnf(157,negated_conjecture,
    false1 != false2,
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(158,plain,
    lazy_impl(true,f7(esk4_0)) = false2,
    inference(rw,[status(thm)],[145,38,theory(equality)]),
    [unfolding] ).

cnf(162,plain,
    ( lazy_impl(true,X1) = X1
    | lazy_impl(true,X1) = err ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[153,38,theory(equality)]),38,theory(equality)]),
    [unfolding] ).

cnf(164,plain,
    ( lazy_impl(X1,X2) = lazy_impl(true,X1)
    | bool(X1) ),
    inference(rw,[status(thm)],[41,38,theory(equality)]),
    [unfolding] ).

cnf(166,plain,
    ( lazy_impl(true,X1) = X1
    | ~ d(X1) ),
    inference(rw,[status(thm)],[154,38,theory(equality)]),
    [unfolding] ).

cnf(168,plain,
    lazy_impl(true,lazy_impl(prop(esk4_0),esk4_0)) = false2,
    inference(rw,[status(thm)],[158,89,theory(equality)]),
    [unfolding] ).

cnf(169,plain,
    ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk4_0),esk4_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[146,89,theory(equality)]),89,theory(equality)]),
    [unfolding] ).

cnf(174,negated_conjecture,
    false != false2,
    inference(rw,[status(thm)],[157,140,theory(equality)]) ).

cnf(180,plain,
    ( lazy_impl(true,lazy_impl(false,esk4_0)) = false2
    | bool(esk4_0) ),
    inference(spm,[status(thm)],[168,92,theory(equality)]) ).

cnf(181,plain,
    ( lazy_impl(true,lazy_impl(true,esk4_0)) = false2
    | ~ bool(esk4_0) ),
    inference(spm,[status(thm)],[168,149,theory(equality)]) ).

cnf(182,plain,
    ( lazy_impl(true,true) = false2
    | bool(esk4_0) ),
    inference(rw,[status(thm)],[180,36,theory(equality)]) ).

cnf(189,plain,
    ( lazy_impl(true,X3) = err
    | X3 != err ),
    inference(ef,[status(thm)],[162,theory(equality)]) ).

cnf(190,plain,
    ( lazy_impl(prop(esk4_0),esk4_0) = false2
    | lazy_impl(true,lazy_impl(prop(esk4_0),esk4_0)) = err ),
    inference(spm,[status(thm)],[168,162,theory(equality)]) ).

cnf(193,plain,
    ( lazy_impl(prop(esk4_0),esk4_0) = false2
    | false2 = err ),
    inference(rw,[status(thm)],[190,168,theory(equality)]) ).

cnf(202,plain,
    ( lazy_impl(true,false) = true
    | bool(false) ),
    inference(spm,[status(thm)],[36,164,theory(equality)]) ).

cnf(337,plain,
    ( false2 = true
    | bool(esk4_0)
    | ~ d(true) ),
    inference(spm,[status(thm)],[166,182,theory(equality)]) ).

cnf(344,plain,
    ( false2 = true
    | bool(esk4_0)
    | $false ),
    inference(rw,[status(thm)],[337,96,theory(equality)]) ).

cnf(345,plain,
    ( false2 = true
    | bool(esk4_0) ),
    inference(cn,[status(thm)],[344,theory(equality)]) ).

cnf(350,plain,
    ( false2 = err
    | false2 = lazy_impl(true,esk4_0)
    | ~ bool(esk4_0) ),
    inference(spm,[status(thm)],[162,181,theory(equality)]) ).

cnf(377,plain,
    ( true = esk4_0
    | false = esk4_0
    | false2 = true ),
    inference(spm,[status(thm)],[102,345,theory(equality)]) ).

cnf(380,plain,
    ( true = false
    | bool(false)
    | ~ d(false) ),
    inference(spm,[status(thm)],[166,202,theory(equality)]) ).

cnf(387,plain,
    ( true = false
    | bool(false)
    | $false ),
    inference(rw,[status(thm)],[380,95,theory(equality)]) ).

cnf(388,plain,
    ( true = false
    | bool(false) ),
    inference(cn,[status(thm)],[387,theory(equality)]) ).

cnf(389,plain,
    bool(false),
    inference(sr,[status(thm)],[388,139,theory(equality)]) ).

cnf(446,plain,
    ( false2 = err
    | ~ forallprefers(lazy_impl(prop(X1),X1),false2) ),
    inference(spm,[status(thm)],[169,193,theory(equality)]) ).

cnf(492,plain,
    ( false2 = err
    | false != lazy_impl(prop(X1),X1)
    | true != false2 ),
    inference(spm,[status(thm)],[446,118,theory(equality)]) ).

cnf(547,plain,
    ( false2 = err
    | lazy_impl(true,X1) != false
    | false2 != true
    | ~ bool(X1) ),
    inference(spm,[status(thm)],[492,149,theory(equality)]) ).

cnf(1465,plain,
    ( false2 = err
    | X1 != false
    | false2 != true
    | ~ bool(X1)
    | ~ d(X1) ),
    inference(spm,[status(thm)],[547,166,theory(equality)]) ).

cnf(1498,plain,
    ( false2 = err
    | false2 = esk4_0
    | ~ bool(esk4_0) ),
    inference(spm,[status(thm)],[162,350,theory(equality)]) ).

cnf(1501,plain,
    ( false2 = err
    | esk4_0 != err
    | ~ bool(esk4_0) ),
    inference(spm,[status(thm)],[189,350,theory(equality)]) ).

cnf(1647,plain,
    ( false2 = esk4_0
    | false2 = err
    | true != esk4_0 ),
    inference(spm,[status(thm)],[1498,100,theory(equality)]) ).

cnf(1769,plain,
    ( false2 = err
    | esk4_0 != err
    | true != esk4_0 ),
    inference(spm,[status(thm)],[1501,100,theory(equality)]) ).

cnf(1774,plain,
    ( false2 = err
    | false2 != true
    | X1 != false
    | ~ d(X1) ),
    inference(csr,[status(thm)],[1465,101]) ).

cnf(1775,plain,
    ( false2 = err
    | false2 != true ),
    inference(spm,[status(thm)],[1774,95,theory(equality)]) ).

cnf(1783,plain,
    ( true = err
    | esk4_0 = false
    | esk4_0 = true ),
    inference(spm,[status(thm)],[1775,377,theory(equality)]) ).

cnf(1785,plain,
    ( esk4_0 = err
    | false2 = err
    | esk4_0 != true ),
    inference(spm,[status(thm)],[1775,1647,theory(equality)]) ).

cnf(1786,plain,
    ( esk4_0 = false
    | esk4_0 = true ),
    inference(sr,[status(thm)],[1783,138,theory(equality)]) ).

cnf(1800,plain,
    ( false2 = false
    | false2 = err
    | esk4_0 = true
    | ~ bool(false) ),
    inference(spm,[status(thm)],[1498,1786,theory(equality)]) ).

cnf(1812,plain,
    ( false2 = false
    | false2 = err
    | esk4_0 = true
    | $false ),
    inference(rw,[status(thm)],[1800,389,theory(equality)]) ).

cnf(1813,plain,
    ( false2 = false
    | false2 = err
    | esk4_0 = true ),
    inference(cn,[status(thm)],[1812,theory(equality)]) ).

cnf(1814,plain,
    ( false2 = err
    | esk4_0 = true ),
    inference(sr,[status(thm)],[1813,174,theory(equality)]) ).

cnf(1884,plain,
    ( esk4_0 = err
    | false2 = err ),
    inference(csr,[status(thm)],[1785,1814]) ).

cnf(1893,plain,
    ( false2 = err
    | esk4_0 != err ),
    inference(csr,[status(thm)],[1769,1814]) ).

cnf(1894,plain,
    false2 = err,
    inference(csr,[status(thm)],[1893,1884]) ).

cnf(1946,plain,
    ( err = true
    | bool(esk4_0) ),
    inference(rw,[status(thm)],[345,1894,theory(equality)]) ).

cnf(1947,plain,
    bool(esk4_0),
    inference(sr,[status(thm)],[1946,138,theory(equality)]) ).

cnf(1948,plain,
    ( lazy_impl(true,lazy_impl(true,esk4_0)) = err
    | ~ bool(esk4_0) ),
    inference(rw,[status(thm)],[181,1894,theory(equality)]) ).

cnf(2113,plain,
    ( lazy_impl(true,lazy_impl(true,esk4_0)) = err
    | $false ),
    inference(rw,[status(thm)],[1948,1947,theory(equality)]) ).

cnf(2114,plain,
    lazy_impl(true,lazy_impl(true,esk4_0)) = err,
    inference(cn,[status(thm)],[2113,theory(equality)]) ).

cnf(2118,plain,
    lazy_impl(true,esk4_0) = err,
    inference(spm,[status(thm)],[2114,162,theory(equality)]) ).

cnf(2161,plain,
    ( err = esk4_0
    | ~ d(esk4_0) ),
    inference(spm,[status(thm)],[166,2118,theory(equality)]) ).

cnf(2181,plain,
    ( false = err
    | esk4_0 = true
    | ~ d(false) ),
    inference(spm,[status(thm)],[2161,1786,theory(equality)]) ).

cnf(2182,plain,
    ( false = err
    | esk4_0 = true
    | $false ),
    inference(rw,[status(thm)],[2181,95,theory(equality)]) ).

cnf(2183,plain,
    ( false = err
    | esk4_0 = true ),
    inference(cn,[status(thm)],[2182,theory(equality)]) ).

cnf(2184,plain,
    esk4_0 = true,
    inference(sr,[status(thm)],[2183,137,theory(equality)]) ).

cnf(2189,plain,
    ( true = err
    | ~ d(esk4_0) ),
    inference(rw,[status(thm)],[2161,2184,theory(equality)]) ).

cnf(2190,plain,
    ( true = err
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2189,2184,theory(equality)]),96,theory(equality)]) ).

cnf(2191,plain,
    true = err,
    inference(cn,[status(thm)],[2190,theory(equality)]) ).

cnf(2192,plain,
    $false,
    inference(sr,[status(thm)],[2191,138,theory(equality)]) ).

cnf(2193,plain,
    $false,
    2192,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW101+1.p
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpigo5AL/sel_SWW101+1.p_1 with time limit 29
% -prover status CounterSatisfiable
% -running prover on /tmp/tmpigo5AL/sel_SWW101+1.p_2 with time limit 89
% -prover status CounterSatisfiable
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpigo5AL/sel_SWW101+1.p_3 with time limit 119
% -prover status CounterSatisfiable
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpigo5AL/sel_SWW101+1.p_4 with time limit 149
% -prover status CounterSatisfiable
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpigo5AL/sel_SWW101+1.p_5 with time limit 299
% -prover status Theorem
% Problem SWW101+1.p solved in phase 4.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW101+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW101+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
% 
%------------------------------------------------------------------------------