%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET894+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:44:36 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 19 unt; 0 def)
% Number of atoms : 280 ( 131 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 353 ( 135 ~; 154 |; 59 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 206 ( 0 sgn 90 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2] : cartesian_product2(singleton(X1),singleton(X2)) = singleton(ordered_pair(X1,X2)),
file('/tmp/tmpWehOHs/sel_SET894+1.p_1',t35_zfmisc_1) ).
fof(2,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmpWehOHs/sel_SET894+1.p_1',l55_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpWehOHs/sel_SET894+1.p_1',d5_tarski) ).
fof(4,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/tmp/tmpWehOHs/sel_SET894+1.p_1',d2_zfmisc_1) ).
fof(8,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpWehOHs/sel_SET894+1.p_1',commutativity_k2_tarski) ).
fof(9,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpWehOHs/sel_SET894+1.p_1',d1_tarski) ).
fof(12,negated_conjecture,
~ ! [X1,X2] : cartesian_product2(singleton(X1),singleton(X2)) = singleton(ordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[1]) ).
fof(16,negated_conjecture,
? [X1,X2] : cartesian_product2(singleton(X1),singleton(X2)) != singleton(ordered_pair(X1,X2)),
inference(fof_nnf,[status(thm)],[12]) ).
fof(17,negated_conjecture,
? [X3,X4] : cartesian_product2(singleton(X3),singleton(X4)) != singleton(ordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[16]) ).
fof(18,negated_conjecture,
cartesian_product2(singleton(esk1_0),singleton(esk2_0)) != singleton(ordered_pair(esk1_0,esk2_0)),
inference(skolemize,[status(esa)],[17]) ).
cnf(19,negated_conjecture,
cartesian_product2(singleton(esk1_0),singleton(esk2_0)) != singleton(ordered_pair(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ( in(X1,X3)
& in(X2,X4) ) )
& ( ~ in(X1,X3)
| ~ in(X2,X4)
| in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(21,plain,
! [X5,X6,X7,X8] :
( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
| ( in(X5,X7)
& in(X6,X8) ) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,plain,
! [X5,X6,X7,X8] :
( ( in(X5,X7)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( in(X6,X8)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
& ( ~ in(X5,X7)
| ~ in(X6,X8)
| in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(23,plain,
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(26,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[3]) ).
cnf(27,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[26]) ).
fof(28,plain,
! [X1,X2,X3] :
( ( X3 != cartesian_product2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) )
& ( ! [X5,X6] :
( ~ in(X5,X1)
| ~ in(X6,X2)
| X4 != ordered_pair(X5,X6) )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ! [X5,X6] :
( ~ in(X5,X1)
| ~ in(X6,X2)
| X4 != ordered_pair(X5,X6) ) )
& ( in(X4,X3)
| ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) )
| X3 = cartesian_product2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(29,plain,
! [X7,X8,X9] :
( ( X9 != cartesian_product2(X7,X8)
| ! [X10] :
( ( ~ in(X10,X9)
| ? [X11,X12] :
( in(X11,X7)
& in(X12,X8)
& X10 = ordered_pair(X11,X12) ) )
& ( ! [X13,X14] :
( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14) )
| in(X10,X9) ) ) )
& ( ? [X15] :
( ( ~ in(X15,X9)
| ! [X16,X17] :
( ~ in(X16,X7)
| ~ in(X17,X8)
| X15 != ordered_pair(X16,X17) ) )
& ( in(X15,X9)
| ? [X18,X19] :
( in(X18,X7)
& in(X19,X8)
& X15 = ordered_pair(X18,X19) ) ) )
| X9 = cartesian_product2(X7,X8) ) ),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,plain,
! [X7,X8,X9] :
( ( X9 != cartesian_product2(X7,X8)
| ! [X10] :
( ( ~ in(X10,X9)
| ( in(esk3_4(X7,X8,X9,X10),X7)
& in(esk4_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk3_4(X7,X8,X9,X10),esk4_4(X7,X8,X9,X10)) ) )
& ( ! [X13,X14] :
( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14) )
| in(X10,X9) ) ) )
& ( ( ( ~ in(esk5_3(X7,X8,X9),X9)
| ! [X16,X17] :
( ~ in(X16,X7)
| ~ in(X17,X8)
| esk5_3(X7,X8,X9) != ordered_pair(X16,X17) ) )
& ( in(esk5_3(X7,X8,X9),X9)
| ( in(esk6_3(X7,X8,X9),X7)
& in(esk7_3(X7,X8,X9),X8)
& esk5_3(X7,X8,X9) = ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)) ) ) )
| X9 = cartesian_product2(X7,X8) ) ),
inference(skolemize,[status(esa)],[29]) ).
fof(31,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk5_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk5_3(X7,X8,X9),X9) )
& ( in(esk5_3(X7,X8,X9),X9)
| ( in(esk6_3(X7,X8,X9),X7)
& in(esk7_3(X7,X8,X9),X8)
& esk5_3(X7,X8,X9) = ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9)) ) ) )
| X9 = cartesian_product2(X7,X8) )
& ( ( ( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14)
| in(X10,X9) )
& ( ~ in(X10,X9)
| ( in(esk3_4(X7,X8,X9,X10),X7)
& in(esk4_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk3_4(X7,X8,X9,X10),esk4_4(X7,X8,X9,X10)) ) ) )
| X9 != cartesian_product2(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[30]) ).
fof(32,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk5_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk5_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk6_3(X7,X8,X9),X7)
| in(esk5_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk7_3(X7,X8,X9),X8)
| in(esk5_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( esk5_3(X7,X8,X9) = ordered_pair(esk6_3(X7,X8,X9),esk7_3(X7,X8,X9))
| in(esk5_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14)
| in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk3_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk4_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk3_4(X7,X8,X9,X10),esk4_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(33,plain,
( X4 = ordered_pair(esk3_4(X2,X3,X1,X4),esk4_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,plain,
( in(esk4_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(35,plain,
( in(esk3_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(52,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[8]) ).
cnf(53,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[52]) ).
fof(54,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(55,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[54]) ).
fof(56,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) != X4 )
& ( in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[55]) ).
fof(57,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) != X4 )
& ( in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[56]) ).
fof(58,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk10_2(X4,X5),X5)
| esk10_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[57]) ).
cnf(59,plain,
( X1 = singleton(X2)
| esk10_2(X2,X1) = X2
| in(esk10_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(60,plain,
( X1 = singleton(X2)
| esk10_2(X2,X1) != X2
| ~ in(esk10_2(X2,X1),X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(61,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(62,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[58]) ).
cnf(72,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[23,27,theory(equality)]),
[unfolding] ).
cnf(73,plain,
( unordered_pair(unordered_pair(esk3_4(X2,X3,X1,X4),esk4_4(X2,X3,X1,X4)),singleton(esk3_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[33,27,theory(equality)]),
[unfolding] ).
cnf(77,negated_conjecture,
cartesian_product2(singleton(esk1_0),singleton(esk2_0)) != singleton(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0))),
inference(rw,[status(thm)],[19,27,theory(equality)]),
[unfolding] ).
cnf(82,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[61,theory(equality)]) ).
cnf(101,plain,
( X1 = esk3_4(X2,X3,X4,X5)
| singleton(X1) != X2
| cartesian_product2(X2,X3) != X4
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[62,35,theory(equality)]) ).
cnf(103,plain,
( X1 = esk4_4(X2,X3,X4,X5)
| singleton(X1) != X3
| cartesian_product2(X2,X3) != X4
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[62,34,theory(equality)]) ).
cnf(106,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[72,53,theory(equality)]) ).
cnf(126,plain,
( unordered_pair(singleton(esk3_4(X2,X3,X1,X4)),unordered_pair(esk3_4(X2,X3,X1,X4),esk4_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[73,53,theory(equality)]) ).
cnf(140,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[82,theory(equality)]) ).
cnf(254,plain,
( X1 = esk3_4(singleton(X1),X2,X3,X4)
| cartesian_product2(singleton(X1),X2) != X3
| ~ in(X4,X3) ),
inference(er,[status(thm)],[101,theory(equality)]) ).
cnf(256,plain,
( unordered_pair(singleton(X1),unordered_pair(X1,esk4_4(singleton(X1),X2,X3,X4))) = X4
| cartesian_product2(singleton(X1),X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[126,254,theory(equality)]) ).
cnf(259,plain,
( X1 = esk4_4(X2,singleton(X1),X3,X4)
| cartesian_product2(X2,singleton(X1)) != X3
| ~ in(X4,X3) ),
inference(er,[status(thm)],[103,theory(equality)]) ).
cnf(542,plain,
( unordered_pair(singleton(X1),unordered_pair(X1,X2)) = X4
| cartesian_product2(singleton(X1),singleton(X2)) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[256,259,theory(equality)]) ).
cnf(561,plain,
( unordered_pair(singleton(X1),unordered_pair(X1,X2)) = X3
| ~ in(X3,cartesian_product2(singleton(X1),singleton(X2))) ),
inference(er,[status(thm)],[542,theory(equality)]) ).
cnf(563,plain,
( unordered_pair(singleton(X1),unordered_pair(X1,X2)) = esk10_2(X3,cartesian_product2(singleton(X1),singleton(X2)))
| esk10_2(X3,cartesian_product2(singleton(X1),singleton(X2))) = X3
| singleton(X3) = cartesian_product2(singleton(X1),singleton(X2)) ),
inference(spm,[status(thm)],[561,59,theory(equality)]) ).
cnf(587,plain,
( esk10_2(X6,cartesian_product2(singleton(X4),singleton(X5))) = X6
| singleton(X6) = cartesian_product2(singleton(X4),singleton(X5))
| unordered_pair(singleton(X4),unordered_pair(X4,X5)) != X6 ),
inference(ef,[status(thm)],[563,theory(equality)]) ).
cnf(700,plain,
( esk10_2(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(singleton(X1),singleton(X2))) = unordered_pair(singleton(X1),unordered_pair(X1,X2))
| singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2)) ),
inference(er,[status(thm)],[587,theory(equality)]) ).
cnf(721,plain,
( singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(singleton(X1),singleton(X2))) ),
inference(spm,[status(thm)],[60,700,theory(equality)]) ).
cnf(1130,plain,
( singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2))
| ~ in(X2,singleton(X2))
| ~ in(X1,singleton(X1)) ),
inference(spm,[status(thm)],[721,106,theory(equality)]) ).
cnf(1144,plain,
( singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2))
| $false
| ~ in(X1,singleton(X1)) ),
inference(rw,[status(thm)],[1130,140,theory(equality)]) ).
cnf(1145,plain,
( singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2))
| $false
| $false ),
inference(rw,[status(thm)],[1144,140,theory(equality)]) ).
cnf(1146,plain,
singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))) = cartesian_product2(singleton(X1),singleton(X2)),
inference(cn,[status(thm)],[1145,theory(equality)]) ).
cnf(1152,plain,
singleton(unordered_pair(unordered_pair(X1,X2),singleton(X1))) = cartesian_product2(singleton(X1),singleton(X2)),
inference(spm,[status(thm)],[1146,53,theory(equality)]) ).
cnf(1679,negated_conjecture,
$false,
inference(rw,[status(thm)],[77,1152,theory(equality)]) ).
cnf(1680,negated_conjecture,
$false,
inference(cn,[status(thm)],[1679,theory(equality)]) ).
cnf(1681,negated_conjecture,
$false,
1680,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET894+1.p
% --creating new selector for []
% -running prover on /tmp/tmpWehOHs/sel_SET894+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET894+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET894+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET894+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
%
%------------------------------------------------------------------------------