TSTP Solution File: SWW102+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWW102+1 : TPTP v5.2.0. Released v5.2.0.
% 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 : Mon Feb 28 18:33:01 EST 2011
% Result : Theorem 1.03s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 19
% Syntax : Number of formulae : 156 ( 44 unt; 0 def)
% Number of atoms : 455 ( 243 equ)
% Maximal formula atoms : 75 ( 2 avg)
% Number of connectives : 455 ( 156 ~; 215 |; 72 &)
% ( 6 <=>; 6 =>; 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 : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 94 ( 4 sgn 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : lazy_impl(false,X1) = true,
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',lazy_impl_axiom2) ).
fof(2,axiom,
! [X1] : lazy_impl(true,X1) = phi(X1),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',lazy_impl_axiom3) ).
fof(4,axiom,
not1(true) = false,
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',not1_axiom3) ).
fof(7,axiom,
! [X2] :
( ~ bool(X2)
=> not1(X2) = phi(X2) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',not1_axiom1) ).
fof(9,axiom,
! [X5] : not2(X5) = impl(X5,false2),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',def_not2) ).
fof(13,axiom,
! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',def_f7) ).
fof(14,axiom,
! [X3] :
( prop(X3) = false
<=> ~ bool(X3) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',prop_false) ).
fof(15,axiom,
( d(true)
& d(false)
& d(err) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',false_true_err_in_d) ).
fof(16,axiom,
! [X3] :
( bool(X3)
<=> ( X3 = false
| X3 = true ) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',def_bool) ).
fof(17,axiom,
! [X1] :
( bool(X1)
=> impl(true,X1) = X1 ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',impl_axiom4) ).
fof(19,axiom,
! [X1] :
( bool(X1)
=> impl(false,X1) = true ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',impl_axiom3) ).
fof(20,axiom,
not1(false) = true,
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',not1_axiom2) ).
fof(21,axiom,
! [X2,X1] :
( ~ bool(X2)
=> impl(X2,X1) = phi(X2) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',impl_axiom1) ).
fof(22,axiom,
! [X3,X4] :
( forallprefers(X3,X4)
<=> ( ( ~ d(X3)
& d(X4) )
| ( d(X3)
& d(X4)
& ~ bool(X3)
& bool(X4) )
| ( X3 = false
& X4 = true ) ) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',def_forallprefers) ).
fof(23,axiom,
( true != false
& true != err
& false != err ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',distinct_false_true_err) ).
fof(24,axiom,
? [X5] :
( false2 = phi(f7(X5))
& ~ ? [X9] : forallprefers(f7(X9),f7(X5)) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',def_false2) ).
fof(25,axiom,
! [X3] :
( prop(X3) = true
<=> bool(X3) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',prop_true) ).
fof(26,axiom,
! [X3] :
( ( d(X3)
& phi(X3) = X3 )
| ( ~ d(X3)
& phi(X3) = err ) ),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',def_phi) ).
fof(27,conjecture,
! [X5] : not1(X5) = not2(X5),
file('/tmp/tmpyFO6Rs/sel_SWW102+1.p_5',not1_not2) ).
fof(28,negated_conjecture,
~ ! [X5] : not1(X5) = not2(X5),
inference(assume_negation,[status(cth)],[27]) ).
fof(31,plain,
! [X2] :
( ~ bool(X2)
=> not1(X2) = phi(X2) ),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(32,plain,
! [X3] :
( prop(X3) = false
<=> ~ bool(X3) ),
inference(fof_simplification,[status(thm)],[14,theory(equality)]) ).
fof(34,plain,
! [X2,X1] :
( ~ bool(X2)
=> impl(X2,X1) = phi(X2) ),
inference(fof_simplification,[status(thm)],[21,theory(equality)]) ).
fof(35,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)],[22,theory(equality)]) ).
fof(36,plain,
! [X3] :
( ( d(X3)
& phi(X3) = X3 )
| ( ~ d(X3)
& phi(X3) = err ) ),
inference(fof_simplification,[status(thm)],[26,theory(equality)]) ).
fof(37,plain,
! [X2] : lazy_impl(false,X2) = true,
inference(variable_rename,[status(thm)],[1]) ).
cnf(38,plain,
lazy_impl(false,X1) = true,
inference(split_conjunct,[status(thm)],[37]) ).
fof(39,plain,
! [X2] : lazy_impl(true,X2) = phi(X2),
inference(variable_rename,[status(thm)],[2]) ).
cnf(40,plain,
lazy_impl(true,X1) = phi(X1),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(44,plain,
not1(true) = false,
inference(split_conjunct,[status(thm)],[4]) ).
fof(73,plain,
! [X2] :
( bool(X2)
| not1(X2) = phi(X2) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(74,plain,
! [X3] :
( bool(X3)
| not1(X3) = phi(X3) ),
inference(variable_rename,[status(thm)],[73]) ).
cnf(75,plain,
( not1(X1) = phi(X1)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(82,plain,
! [X6] : not2(X6) = impl(X6,false2),
inference(variable_rename,[status(thm)],[9]) ).
cnf(83,plain,
not2(X1) = impl(X1,false2),
inference(split_conjunct,[status(thm)],[82]) ).
fof(94,plain,
! [X6] : f7(X6) = lazy_impl(prop(X6),X6),
inference(variable_rename,[status(thm)],[13]) ).
cnf(95,plain,
f7(X1) = lazy_impl(prop(X1),X1),
inference(split_conjunct,[status(thm)],[94]) ).
fof(96,plain,
! [X3] :
( ( prop(X3) != false
| ~ bool(X3) )
& ( bool(X3)
| prop(X3) = false ) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(97,plain,
! [X4] :
( ( prop(X4) != false
| ~ bool(X4) )
& ( bool(X4)
| prop(X4) = false ) ),
inference(variable_rename,[status(thm)],[96]) ).
cnf(98,plain,
( prop(X1) = false
| bool(X1) ),
inference(split_conjunct,[status(thm)],[97]) ).
cnf(101,plain,
d(false),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(102,plain,
d(true),
inference(split_conjunct,[status(thm)],[15]) ).
fof(103,plain,
! [X3] :
( ( ~ bool(X3)
| X3 = false
| X3 = true )
& ( ( X3 != false
& X3 != true )
| bool(X3) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(104,plain,
! [X4] :
( ( ~ bool(X4)
| X4 = false
| X4 = true )
& ( ( X4 != false
& X4 != true )
| bool(X4) ) ),
inference(variable_rename,[status(thm)],[103]) ).
fof(105,plain,
! [X4] :
( ( ~ bool(X4)
| X4 = false
| X4 = true )
& ( X4 != false
| bool(X4) )
& ( X4 != true
| bool(X4) ) ),
inference(distribute,[status(thm)],[104]) ).
cnf(107,plain,
( bool(X1)
| X1 != false ),
inference(split_conjunct,[status(thm)],[105]) ).
cnf(108,plain,
( X1 = true
| X1 = false
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[105]) ).
fof(109,plain,
! [X1] :
( ~ bool(X1)
| impl(true,X1) = X1 ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(110,plain,
! [X2] :
( ~ bool(X2)
| impl(true,X2) = X2 ),
inference(variable_rename,[status(thm)],[109]) ).
cnf(111,plain,
( impl(true,X1) = X1
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[110]) ).
fof(115,plain,
! [X1] :
( ~ bool(X1)
| impl(false,X1) = true ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(116,plain,
! [X2] :
( ~ bool(X2)
| impl(false,X2) = true ),
inference(variable_rename,[status(thm)],[115]) ).
cnf(117,plain,
( impl(false,X1) = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(118,plain,
not1(false) = true,
inference(split_conjunct,[status(thm)],[20]) ).
fof(119,plain,
! [X2,X1] :
( bool(X2)
| impl(X2,X1) = phi(X2) ),
inference(fof_nnf,[status(thm)],[34]) ).
fof(120,plain,
! [X3,X4] :
( bool(X3)
| impl(X3,X4) = phi(X3) ),
inference(variable_rename,[status(thm)],[119]) ).
cnf(121,plain,
( impl(X1,X2) = phi(X1)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[120]) ).
fof(122,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)],[35]) ).
fof(123,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)],[122]) ).
fof(124,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)],[123]) ).
cnf(125,plain,
( forallprefers(X1,X2)
| X2 != true
| X1 != false ),
inference(split_conjunct,[status(thm)],[124]) ).
cnf(144,plain,
false != err,
inference(split_conjunct,[status(thm)],[23]) ).
cnf(145,plain,
true != err,
inference(split_conjunct,[status(thm)],[23]) ).
cnf(146,plain,
true != false,
inference(split_conjunct,[status(thm)],[23]) ).
fof(147,plain,
? [X5] :
( false2 = phi(f7(X5))
& ! [X9] : ~ forallprefers(f7(X9),f7(X5)) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(148,plain,
? [X10] :
( false2 = phi(f7(X10))
& ! [X11] : ~ forallprefers(f7(X11),f7(X10)) ),
inference(variable_rename,[status(thm)],[147]) ).
fof(149,plain,
( false2 = phi(f7(esk4_0))
& ! [X11] : ~ forallprefers(f7(X11),f7(esk4_0)) ),
inference(skolemize,[status(esa)],[148]) ).
fof(150,plain,
! [X11] :
( ~ forallprefers(f7(X11),f7(esk4_0))
& false2 = phi(f7(esk4_0)) ),
inference(shift_quantors,[status(thm)],[149]) ).
cnf(151,plain,
false2 = phi(f7(esk4_0)),
inference(split_conjunct,[status(thm)],[150]) ).
cnf(152,plain,
~ forallprefers(f7(X1),f7(esk4_0)),
inference(split_conjunct,[status(thm)],[150]) ).
fof(153,plain,
! [X3] :
( ( prop(X3) != true
| bool(X3) )
& ( ~ bool(X3)
| prop(X3) = true ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(154,plain,
! [X4] :
( ( prop(X4) != true
| bool(X4) )
& ( ~ bool(X4)
| prop(X4) = true ) ),
inference(variable_rename,[status(thm)],[153]) ).
cnf(155,plain,
( prop(X1) = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[154]) ).
fof(157,plain,
! [X4] :
( ( d(X4)
& phi(X4) = X4 )
| ( ~ d(X4)
& phi(X4) = err ) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(158,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)],[157]) ).
cnf(159,plain,
( phi(X1) = X1
| phi(X1) = err ),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(160,plain,
( phi(X1) = X1
| ~ d(X1) ),
inference(split_conjunct,[status(thm)],[158]) ).
cnf(161,plain,
( d(X1)
| phi(X1) = err ),
inference(split_conjunct,[status(thm)],[158]) ).
fof(163,negated_conjecture,
? [X5] : not1(X5) != not2(X5),
inference(fof_nnf,[status(thm)],[28]) ).
fof(164,negated_conjecture,
? [X6] : not1(X6) != not2(X6),
inference(variable_rename,[status(thm)],[163]) ).
fof(165,negated_conjecture,
not1(esk5_0) != not2(esk5_0),
inference(skolemize,[status(esa)],[164]) ).
cnf(166,negated_conjecture,
not1(esk5_0) != not2(esk5_0),
inference(split_conjunct,[status(thm)],[165]) ).
cnf(167,negated_conjecture,
impl(esk5_0,false2) != not1(esk5_0),
inference(rw,[status(thm)],[166,83,theory(equality)]),
[unfolding] ).
cnf(168,plain,
lazy_impl(true,f7(esk4_0)) = false2,
inference(rw,[status(thm)],[151,40,theory(equality)]),
[unfolding] ).
cnf(172,plain,
( lazy_impl(true,X1) = X1
| lazy_impl(true,X1) = err ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[159,40,theory(equality)]),40,theory(equality)]),
[unfolding] ).
cnf(173,plain,
( lazy_impl(true,X1) = err
| d(X1) ),
inference(rw,[status(thm)],[161,40,theory(equality)]),
[unfolding] ).
cnf(174,plain,
( not1(X1) = lazy_impl(true,X1)
| bool(X1) ),
inference(rw,[status(thm)],[75,40,theory(equality)]),
[unfolding] ).
cnf(176,plain,
( impl(X1,X2) = lazy_impl(true,X1)
| bool(X1) ),
inference(rw,[status(thm)],[121,40,theory(equality)]),
[unfolding] ).
cnf(177,plain,
( lazy_impl(true,X1) = X1
| ~ d(X1) ),
inference(rw,[status(thm)],[160,40,theory(equality)]),
[unfolding] ).
cnf(179,plain,
lazy_impl(true,lazy_impl(prop(esk4_0),esk4_0)) = false2,
inference(rw,[status(thm)],[168,95,theory(equality)]),
[unfolding] ).
cnf(180,plain,
~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk4_0),esk4_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[152,95,theory(equality)]),95,theory(equality)]),
[unfolding] ).
cnf(193,plain,
( lazy_impl(true,lazy_impl(false,esk4_0)) = false2
| bool(esk4_0) ),
inference(spm,[status(thm)],[179,98,theory(equality)]) ).
cnf(194,plain,
( lazy_impl(true,lazy_impl(true,esk4_0)) = false2
| ~ bool(esk4_0) ),
inference(spm,[status(thm)],[179,155,theory(equality)]) ).
cnf(195,plain,
( false2 = lazy_impl(prop(esk4_0),esk4_0)
| ~ d(lazy_impl(prop(esk4_0),esk4_0)) ),
inference(spm,[status(thm)],[177,179,theory(equality)]) ).
cnf(196,plain,
( false2 = err
| d(lazy_impl(prop(esk4_0),esk4_0)) ),
inference(spm,[status(thm)],[173,179,theory(equality)]) ).
cnf(197,plain,
( lazy_impl(true,true) = false2
| bool(esk4_0) ),
inference(rw,[status(thm)],[193,38,theory(equality)]) ).
cnf(204,plain,
( lazy_impl(true,false) = true
| bool(false) ),
inference(spm,[status(thm)],[118,174,theory(equality)]) ).
cnf(206,negated_conjecture,
( bool(esk5_0)
| lazy_impl(true,esk5_0) != impl(esk5_0,false2) ),
inference(spm,[status(thm)],[167,174,theory(equality)]) ).
cnf(325,negated_conjecture,
bool(esk5_0),
inference(csr,[status(thm)],[206,176]) ).
cnf(326,negated_conjecture,
( true = esk5_0
| false = esk5_0 ),
inference(spm,[status(thm)],[108,325,theory(equality)]) ).
cnf(329,negated_conjecture,
( esk5_0 = true
| not1(false) != impl(false,false2) ),
inference(spm,[status(thm)],[167,326,theory(equality)]) ).
cnf(330,negated_conjecture,
( esk5_0 = true
| true != impl(false,false2) ),
inference(rw,[status(thm)],[329,118,theory(equality)]) ).
cnf(331,negated_conjecture,
( esk5_0 = true
| ~ bool(false2) ),
inference(spm,[status(thm)],[330,117,theory(equality)]) ).
cnf(334,plain,
( false2 = true
| bool(esk4_0)
| ~ d(true) ),
inference(spm,[status(thm)],[177,197,theory(equality)]) ).
cnf(339,plain,
( false2 = true
| bool(esk4_0)
| $false ),
inference(rw,[status(thm)],[334,102,theory(equality)]) ).
cnf(340,plain,
( false2 = true
| bool(esk4_0) ),
inference(cn,[status(thm)],[339,theory(equality)]) ).
cnf(342,negated_conjecture,
( esk5_0 = true
| false != false2 ),
inference(spm,[status(thm)],[331,107,theory(equality)]) ).
cnf(345,negated_conjecture,
( not1(true) != impl(true,false2)
| false2 != false ),
inference(spm,[status(thm)],[167,342,theory(equality)]) ).
cnf(346,negated_conjecture,
( false != impl(true,false2)
| false2 != false ),
inference(rw,[status(thm)],[345,44,theory(equality)]) ).
cnf(350,plain,
( true = esk4_0
| false = esk4_0
| false2 = true ),
inference(spm,[status(thm)],[108,340,theory(equality)]) ).
cnf(357,plain,
( false2 = err
| false2 = lazy_impl(true,esk4_0)
| ~ bool(esk4_0) ),
inference(spm,[status(thm)],[172,194,theory(equality)]) ).
cnf(361,negated_conjecture,
( false2 != false
| ~ bool(false2) ),
inference(spm,[status(thm)],[346,111,theory(equality)]) ).
cnf(365,negated_conjecture,
false2 != false,
inference(csr,[status(thm)],[361,107]) ).
cnf(376,plain,
( true = false
| bool(false)
| ~ d(false) ),
inference(spm,[status(thm)],[177,204,theory(equality)]) ).
cnf(380,plain,
( true = false
| bool(false)
| $false ),
inference(rw,[status(thm)],[376,101,theory(equality)]) ).
cnf(381,plain,
( true = false
| bool(false) ),
inference(cn,[status(thm)],[380,theory(equality)]) ).
cnf(382,plain,
bool(false),
inference(sr,[status(thm)],[381,146,theory(equality)]) ).
cnf(421,plain,
( lazy_impl(prop(esk4_0),esk4_0) = false2
| false2 = err ),
inference(spm,[status(thm)],[195,196,theory(equality)]) ).
cnf(433,plain,
( false2 = err
| ~ forallprefers(lazy_impl(prop(X1),X1),false2) ),
inference(spm,[status(thm)],[180,421,theory(equality)]) ).
cnf(467,plain,
( false2 = err
| false != lazy_impl(prop(X1),X1)
| true != false2 ),
inference(spm,[status(thm)],[433,125,theory(equality)]) ).
cnf(496,plain,
( false2 = err
| lazy_impl(true,X1) != false
| false2 != true
| ~ bool(X1) ),
inference(spm,[status(thm)],[467,155,theory(equality)]) ).
cnf(521,plain,
( false2 = err
| X1 != false
| false2 != true
| ~ bool(X1)
| ~ d(X1) ),
inference(spm,[status(thm)],[496,177,theory(equality)]) ).
cnf(564,plain,
( false2 = err
| false2 = esk4_0
| ~ bool(esk4_0) ),
inference(spm,[status(thm)],[172,357,theory(equality)]) ).
cnf(582,plain,
( false2 = err
| false2 != true
| X1 != false
| ~ d(X1) ),
inference(csr,[status(thm)],[521,107]) ).
cnf(583,plain,
( false2 = err
| false2 != true ),
inference(spm,[status(thm)],[582,101,theory(equality)]) ).
cnf(588,plain,
( true = err
| esk4_0 = false
| esk4_0 = true ),
inference(spm,[status(thm)],[583,350,theory(equality)]) ).
cnf(589,plain,
( esk4_0 = false
| esk4_0 = true ),
inference(sr,[status(thm)],[588,145,theory(equality)]) ).
cnf(600,plain,
( lazy_impl(true,false) = false2
| false2 = err
| esk4_0 = true
| ~ bool(false) ),
inference(spm,[status(thm)],[357,589,theory(equality)]) ).
cnf(604,plain,
( lazy_impl(true,false) = false2
| false2 = err
| esk4_0 = true
| $false ),
inference(rw,[status(thm)],[600,382,theory(equality)]) ).
cnf(605,plain,
( lazy_impl(true,false) = false2
| false2 = err
| esk4_0 = true ),
inference(cn,[status(thm)],[604,theory(equality)]) ).
cnf(614,plain,
( false2 = false
| esk4_0 = true
| false2 = err
| ~ d(false) ),
inference(spm,[status(thm)],[177,605,theory(equality)]) ).
cnf(620,plain,
( false2 = false
| esk4_0 = true
| false2 = err
| $false ),
inference(rw,[status(thm)],[614,101,theory(equality)]) ).
cnf(621,plain,
( false2 = false
| esk4_0 = true
| false2 = err ),
inference(cn,[status(thm)],[620,theory(equality)]) ).
cnf(622,plain,
( esk4_0 = true
| false2 = err ),
inference(sr,[status(thm)],[621,365,theory(equality)]) ).
cnf(814,plain,
( false2 = esk4_0
| false2 = err
| false2 = true ),
inference(spm,[status(thm)],[564,340,theory(equality)]) ).
cnf(821,plain,
( false2 = esk4_0
| false2 = err ),
inference(csr,[status(thm)],[814,583]) ).
cnf(822,plain,
( false2 = err
| esk4_0 != err ),
inference(ef,[status(thm)],[821,theory(equality)]) ).
cnf(833,plain,
( esk4_0 = err
| false2 = err
| esk4_0 != true ),
inference(spm,[status(thm)],[583,821,theory(equality)]) ).
cnf(938,plain,
( esk4_0 = err
| false2 = err ),
inference(csr,[status(thm)],[833,622]) ).
cnf(939,plain,
false2 = err,
inference(csr,[status(thm)],[938,822]) ).
cnf(983,plain,
( lazy_impl(true,lazy_impl(true,esk4_0)) = err
| ~ bool(esk4_0) ),
inference(rw,[status(thm)],[194,939,theory(equality)]) ).
cnf(984,plain,
( err = true
| bool(esk4_0) ),
inference(rw,[status(thm)],[340,939,theory(equality)]) ).
cnf(985,plain,
bool(esk4_0),
inference(sr,[status(thm)],[984,145,theory(equality)]) ).
cnf(1121,plain,
( lazy_impl(true,lazy_impl(true,esk4_0)) = err
| $false ),
inference(rw,[status(thm)],[983,985,theory(equality)]) ).
cnf(1122,plain,
lazy_impl(true,lazy_impl(true,esk4_0)) = err,
inference(cn,[status(thm)],[1121,theory(equality)]) ).
cnf(1126,plain,
lazy_impl(true,esk4_0) = err,
inference(spm,[status(thm)],[1122,172,theory(equality)]) ).
cnf(1165,plain,
( err = esk4_0
| ~ d(esk4_0) ),
inference(spm,[status(thm)],[177,1126,theory(equality)]) ).
cnf(1186,plain,
( false = err
| esk4_0 = true
| ~ d(false) ),
inference(spm,[status(thm)],[1165,589,theory(equality)]) ).
cnf(1187,plain,
( false = err
| esk4_0 = true
| $false ),
inference(rw,[status(thm)],[1186,101,theory(equality)]) ).
cnf(1188,plain,
( false = err
| esk4_0 = true ),
inference(cn,[status(thm)],[1187,theory(equality)]) ).
cnf(1189,plain,
esk4_0 = true,
inference(sr,[status(thm)],[1188,144,theory(equality)]) ).
cnf(1194,plain,
( true = err
| ~ d(esk4_0) ),
inference(rw,[status(thm)],[1165,1189,theory(equality)]) ).
cnf(1195,plain,
( true = err
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[1194,1189,theory(equality)]),102,theory(equality)]) ).
cnf(1196,plain,
true = err,
inference(cn,[status(thm)],[1195,theory(equality)]) ).
cnf(1197,plain,
$false,
inference(sr,[status(thm)],[1196,145,theory(equality)]) ).
cnf(1198,plain,
$false,
1197,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW102+1.p
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpyFO6Rs/sel_SWW102+1.p_1 with time limit 29
% -prover status CounterSatisfiable
% -running prover on /tmp/tmpyFO6Rs/sel_SWW102+1.p_2 with time limit 89
% -prover status CounterSatisfiable
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpyFO6Rs/sel_SWW102+1.p_3 with time limit 119
% -prover status CounterSatisfiable
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpyFO6Rs/sel_SWW102+1.p_4 with time limit 149
% -prover status CounterSatisfiable
% --creating new selector for [SWV012+0.ax]
% -running prover on /tmp/tmpyFO6Rs/sel_SWW102+1.p_5 with time limit 299
% -prover status Theorem
% Problem SWW102+1.p solved in phase 4.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW102+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW102+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
%
%------------------------------------------------------------------------------