TSTP Solution File: SET159+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET159+3 : TPTP v5.0.0. Released v2.2.0.
% 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 : Sun Dec 26 02:52:29 EST 2010
% Result : Theorem 14.22s
% Output : CNFRefutation 14.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 106 ( 50 unt; 0 def)
% Number of atoms : 217 ( 52 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 177 ( 66 ~; 84 |; 23 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 288 ( 16 sgn 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmphmCHi2/sel_SET159+3.p_1',commutativity_of_union) ).
fof(2,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmphmCHi2/sel_SET159+3.p_1',equal_defn) ).
fof(3,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmphmCHi2/sel_SET159+3.p_1',union_defn) ).
fof(4,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmphmCHi2/sel_SET159+3.p_1',subset_defn) ).
fof(6,conjecture,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/tmp/tmphmCHi2/sel_SET159+3.p_1',prove_associativity_of_union) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(assume_negation,[status(cth)],[6]) ).
fof(9,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(10,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[9]) ).
fof(11,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(12,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[12]) ).
cnf(14,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[13]) ).
fof(17,plain,
! [X1,X2,X3] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(18,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[17]) ).
fof(19,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(20,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(21,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[19]) ).
cnf(22,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(23,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(24,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[25]) ).
fof(27,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(30,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(40,negated_conjecture,
? [X1,X2,X3] : union(union(X1,X2),X3) != union(X1,union(X2,X3)),
inference(fof_nnf,[status(thm)],[8]) ).
fof(41,negated_conjecture,
? [X4,X5,X6] : union(union(X4,X5),X6) != union(X4,union(X5,X6)),
inference(variable_rename,[status(thm)],[40]) ).
fof(42,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(skolemize,[status(esa)],[41]) ).
cnf(43,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[42]) ).
cnf(46,negated_conjecture,
union(esk5_0,union(esk3_0,esk4_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[43,10,theory(equality)]) ).
cnf(55,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[28,20,theory(equality)]) ).
cnf(56,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[28,21,theory(equality)]) ).
cnf(64,plain,
( member(esk1_2(union(X1,X2),X3),X2)
| member(esk1_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[22,29,theory(equality)]) ).
cnf(74,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[55,20,theory(equality)]) ).
cnf(75,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
inference(spm,[status(thm)],[55,21,theory(equality)]) ).
cnf(76,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[55,29,theory(equality)]) ).
cnf(92,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[56,20,theory(equality)]) ).
cnf(93,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[56,21,theory(equality)]) ).
cnf(102,plain,
( subset(union(X1,X2),X1)
| member(esk1_2(union(X1,X2),X1),X2) ),
inference(spm,[status(thm)],[28,64,theory(equality)]) ).
cnf(106,plain,
( subset(union(X1,X2),union(X3,X1))
| member(esk1_2(union(X1,X2),union(X3,X1)),X2) ),
inference(spm,[status(thm)],[55,64,theory(equality)]) ).
cnf(108,plain,
( subset(union(X1,X2),union(X1,X3))
| member(esk1_2(union(X1,X2),union(X1,X3)),X2) ),
inference(spm,[status(thm)],[56,64,theory(equality)]) ).
cnf(109,plain,
( subset(union(X1,X2),union(X2,X3))
| member(esk1_2(union(X1,X2),union(X2,X3)),X1) ),
inference(spm,[status(thm)],[56,64,theory(equality)]) ).
cnf(168,plain,
( member(esk1_2(union(X1,union(X2,X3)),X1),X3)
| member(esk1_2(union(X1,union(X2,X3)),X1),X2)
| subset(union(X1,union(X2,X3)),X1) ),
inference(spm,[status(thm)],[22,102,theory(equality)]) ).
cnf(169,plain,
subset(union(union(X1,X2),X2),union(X1,X2)),
inference(spm,[status(thm)],[55,102,theory(equality)]) ).
cnf(173,plain,
subset(union(X2,union(X1,X2)),union(X1,X2)),
inference(rw,[status(thm)],[169,10,theory(equality)]) ).
cnf(178,plain,
( union(X1,X2) = union(X2,union(X1,X2))
| ~ subset(union(X1,X2),union(X2,union(X1,X2))) ),
inference(spm,[status(thm)],[14,173,theory(equality)]) ).
cnf(182,plain,
( union(X1,X2) = union(X2,union(X1,X2))
| $false ),
inference(rw,[status(thm)],[178,76,theory(equality)]) ).
cnf(183,plain,
union(X1,X2) = union(X2,union(X1,X2)),
inference(cn,[status(thm)],[182,theory(equality)]) ).
cnf(316,plain,
subset(union(union(X1,union(X2,X3)),X3),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[74,102,theory(equality)]) ).
cnf(318,plain,
subset(union(X3,union(X1,union(X2,X3))),union(X1,union(X2,X3))),
inference(rw,[status(thm)],[316,10,theory(equality)]) ).
cnf(334,plain,
subset(union(union(X1,union(X2,X3)),X2),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[75,102,theory(equality)]) ).
cnf(336,plain,
subset(union(X2,union(X1,union(X2,X3))),union(X1,union(X2,X3))),
inference(rw,[status(thm)],[334,10,theory(equality)]) ).
cnf(453,plain,
( union(X1,union(X2,X3)) = union(X3,union(X1,union(X2,X3)))
| ~ subset(union(X1,union(X2,X3)),union(X3,union(X1,union(X2,X3)))) ),
inference(spm,[status(thm)],[14,318,theory(equality)]) ).
cnf(463,plain,
( union(X1,union(X2,X3)) = union(X3,union(X1,union(X2,X3)))
| $false ),
inference(rw,[status(thm)],[453,76,theory(equality)]) ).
cnf(464,plain,
union(X1,union(X2,X3)) = union(X3,union(X1,union(X2,X3))),
inference(cn,[status(thm)],[463,theory(equality)]) ).
cnf(541,plain,
( union(X1,union(X2,X3)) = union(X2,union(X1,union(X2,X3)))
| ~ subset(union(X1,union(X2,X3)),union(X2,union(X1,union(X2,X3)))) ),
inference(spm,[status(thm)],[14,336,theory(equality)]) ).
cnf(555,plain,
( union(X1,union(X2,X3)) = union(X2,union(X1,union(X2,X3)))
| $false ),
inference(rw,[status(thm)],[541,76,theory(equality)]) ).
cnf(556,plain,
union(X1,union(X2,X3)) = union(X2,union(X1,union(X2,X3))),
inference(cn,[status(thm)],[555,theory(equality)]) ).
cnf(683,plain,
subset(union(union(union(X1,X2),X3),X1),union(union(X1,X2),X3)),
inference(spm,[status(thm)],[93,102,theory(equality)]) ).
cnf(686,plain,
subset(union(X1,union(union(X1,X2),X3)),union(union(X1,X2),X3)),
inference(rw,[status(thm)],[683,10,theory(equality)]) ).
cnf(827,plain,
( union(union(X1,X2),X3) = union(X1,union(union(X1,X2),X3))
| ~ subset(union(union(X1,X2),X3),union(X1,union(union(X1,X2),X3))) ),
inference(spm,[status(thm)],[14,686,theory(equality)]) ).
cnf(844,plain,
( union(union(X1,X2),X3) = union(X1,union(union(X1,X2),X3))
| $false ),
inference(rw,[status(thm)],[827,76,theory(equality)]) ).
cnf(845,plain,
union(union(X1,X2),X3) = union(X1,union(union(X1,X2),X3)),
inference(cn,[status(thm)],[844,theory(equality)]) ).
cnf(1440,plain,
subset(union(X1,X2),union(X2,X1)),
inference(spm,[status(thm)],[56,106,theory(equality)]) ).
cnf(1443,plain,
subset(union(X1,X2),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[92,106,theory(equality)]) ).
cnf(1444,plain,
subset(union(X1,X2),union(union(X2,X3),X1)),
inference(spm,[status(thm)],[93,106,theory(equality)]) ).
cnf(1469,plain,
( member(X1,union(X2,X3))
| ~ member(X1,union(X3,X2)) ),
inference(spm,[status(thm)],[30,1440,theory(equality)]) ).
cnf(1752,plain,
subset(union(X1,X2),union(X1,union(X3,X2))),
inference(spm,[status(thm)],[74,108,theory(equality)]) ).
cnf(1753,plain,
subset(union(X1,X2),union(X1,union(X2,X3))),
inference(spm,[status(thm)],[75,108,theory(equality)]) ).
cnf(1789,plain,
( union(X1,union(X2,X3)) = union(X1,X3)
| ~ subset(union(X1,union(X2,X3)),union(X1,X3)) ),
inference(spm,[status(thm)],[14,1752,theory(equality)]) ).
cnf(1827,plain,
subset(union(X1,X2),union(X1,union(X3,union(X2,X4)))),
inference(spm,[status(thm)],[1753,556,theory(equality)]) ).
cnf(1833,plain,
subset(union(X1,X2),union(X1,union(union(X2,X3),X4))),
inference(spm,[status(thm)],[1753,845,theory(equality)]) ).
cnf(1890,plain,
subset(union(X1,X2),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[74,109,theory(equality)]) ).
cnf(1933,plain,
( union(X1,union(X2,X3)) = union(X3,X1)
| ~ subset(union(X1,union(X2,X3)),union(X3,X1)) ),
inference(spm,[status(thm)],[14,1890,theory(equality)]) ).
cnf(2199,plain,
( member(esk1_2(union(X1,union(X2,X3)),X1),union(X3,X2))
| subset(union(X1,union(X2,X3)),X1) ),
inference(spm,[status(thm)],[1469,102,theory(equality)]) ).
cnf(2800,plain,
( subset(union(union(X1,X2),union(X2,X3)),union(X1,X2))
| member(esk1_2(union(union(X1,X2),union(X2,X3)),union(X1,X2)),X3) ),
inference(spm,[status(thm)],[55,168,theory(equality)]) ).
cnf(4542,plain,
subset(union(X1,X2),union(union(X1,X3),union(X2,X4))),
inference(spm,[status(thm)],[1827,845,theory(equality)]) ).
cnf(4658,plain,
subset(union(X1,X2),union(union(X2,X3),union(X4,X1))),
inference(spm,[status(thm)],[1833,464,theory(equality)]) ).
cnf(189033,plain,
subset(union(union(X1,X2),union(X2,X1)),union(X1,X2)),
inference(spm,[status(thm)],[28,2199,theory(equality)]) ).
cnf(189391,plain,
( union(X1,X2) = union(union(X1,X2),union(X2,X1))
| ~ subset(union(X1,X2),union(union(X1,X2),union(X2,X1))) ),
inference(spm,[status(thm)],[14,189033,theory(equality)]) ).
cnf(189526,plain,
( union(X1,X2) = union(union(X1,X2),union(X2,X1))
| $false ),
inference(rw,[status(thm)],[189391,4542,theory(equality)]) ).
cnf(189527,plain,
union(X1,X2) = union(union(X1,X2),union(X2,X1)),
inference(cn,[status(thm)],[189526,theory(equality)]) ).
cnf(189591,plain,
subset(union(X1,union(X2,X3)),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[1443,189527,theory(equality)]) ).
cnf(189609,plain,
subset(union(union(X1,X2),X3),union(X3,union(X2,X1))),
inference(spm,[status(thm)],[1890,189527,theory(equality)]) ).
cnf(205261,plain,
( union(X1,union(X2,X3)) = union(union(X3,X2),X1)
| ~ subset(union(X1,union(X2,X3)),union(union(X3,X2),X1)) ),
inference(spm,[status(thm)],[14,189609,theory(equality)]) ).
cnf(205535,plain,
( union(X1,union(X2,X3)) = union(union(X3,X2),X1)
| $false ),
inference(rw,[status(thm)],[205261,189591,theory(equality)]) ).
cnf(205536,plain,
union(X1,union(X2,X3)) = union(union(X3,X2),X1),
inference(cn,[status(thm)],[205535,theory(equality)]) ).
cnf(433794,plain,
subset(union(union(union(X1,X2),X3),union(X3,X2)),union(union(X1,X2),X3)),
inference(spm,[status(thm)],[92,2800,theory(equality)]) ).
cnf(434062,plain,
subset(union(union(X3,X2),union(X3,union(X1,X2))),union(union(X1,X2),X3)),
inference(rw,[status(thm)],[433794,205536,theory(equality)]) ).
cnf(434418,plain,
( union(union(X1,X2),X3) = union(union(X3,X2),union(X3,union(X1,X2)))
| ~ subset(union(union(X1,X2),X3),union(union(X3,X2),union(X3,union(X1,X2)))) ),
inference(spm,[status(thm)],[14,434062,theory(equality)]) ).
cnf(434734,plain,
( union(union(X1,X2),X3) = union(union(X3,X2),union(X3,union(X1,X2)))
| $false ),
inference(rw,[status(thm)],[434418,4658,theory(equality)]) ).
cnf(434735,plain,
union(union(X1,X2),X3) = union(union(X3,X2),union(X3,union(X1,X2))),
inference(cn,[status(thm)],[434734,theory(equality)]) ).
cnf(437830,plain,
( union(union(X3,X2),X1) = union(union(X1,X2),union(X3,X2))
| ~ subset(union(union(X3,X2),X1),union(union(X1,X2),union(X3,X2))) ),
inference(spm,[status(thm)],[1789,434735,theory(equality)]) ).
cnf(437839,plain,
( union(union(X3,X2),X1) = union(union(X3,X2),union(X1,X2))
| ~ subset(union(union(X3,X2),X1),union(union(X3,X2),union(X1,X2))) ),
inference(spm,[status(thm)],[1933,434735,theory(equality)]) ).
cnf(440753,plain,
( union(union(X3,X2),X1) = union(union(X1,X2),union(X3,X2))
| $false ),
inference(rw,[status(thm)],[437830,1444,theory(equality)]) ).
cnf(440754,plain,
union(union(X3,X2),X1) = union(union(X1,X2),union(X3,X2)),
inference(cn,[status(thm)],[440753,theory(equality)]) ).
cnf(440762,plain,
( union(union(X3,X2),X1) = union(union(X3,X2),union(X1,X2))
| $false ),
inference(rw,[status(thm)],[437839,1753,theory(equality)]) ).
cnf(440763,plain,
union(union(X3,X2),X1) = union(union(X3,X2),union(X1,X2)),
inference(cn,[status(thm)],[440762,theory(equality)]) ).
cnf(447665,plain,
union(union(X1,X2),X3) = union(union(X3,X2),X1),
inference(rw,[status(thm)],[440763,440754,theory(equality)]) ).
cnf(452740,plain,
union(union(X3,X2),X1) = union(X3,union(X1,X2)),
inference(spm,[status(thm)],[10,447665,theory(equality)]) ).
cnf(457644,plain,
union(X1,union(X3,X2)) = union(union(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[440754,452740,theory(equality)]),10,theory(equality)]),183,theory(equality)]) ).
cnf(457645,plain,
union(X1,union(X3,X2)) = union(X3,union(X1,X2)),
inference(rw,[status(thm)],[457644,452740,theory(equality)]) ).
cnf(460596,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[46,457645,theory(equality)]),10,theory(equality)]) ).
cnf(460597,negated_conjecture,
$false,
inference(cn,[status(thm)],[460596,theory(equality)]) ).
cnf(460598,negated_conjecture,
$false,
460597,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET159+3.p
% --creating new selector for []
% -running prover on /tmp/tmphmCHi2/sel_SET159+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET159+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET159+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET159+3.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
%
%------------------------------------------------------------------------------