TSTP Solution File: SEU157+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU157+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 04:59:30 EST 2010
% Result : Theorem 0.40s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 12 unt; 0 def)
% Number of atoms : 248 ( 96 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 311 ( 122 ~; 133 |; 51 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 201 ( 14 sgn 76 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/tmp/tmpX9Gq5w/sel_SEU157+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/tmpX9Gq5w/sel_SEU157+1.p_1',d5_tarski) ).
fof(6,axiom,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/tmp/tmpX9Gq5w/sel_SEU157+1.p_1',t33_zfmisc_1) ).
fof(9,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpX9Gq5w/sel_SEU157+1.p_1',commutativity_k2_tarski) ).
fof(13,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/tmpX9Gq5w/sel_SEU157+1.p_1',d2_zfmisc_1) ).
fof(14,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
inference(assume_negation,[status(cth)],[1]) ).
fof(18,negated_conjecture,
? [X1,X2,X3,X4] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ in(X1,X3)
| ~ in(X2,X4) )
& ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ( in(X1,X3)
& in(X2,X4) ) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(19,negated_conjecture,
? [X5,X6,X7,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))
| ( in(X5,X7)
& in(X6,X8) ) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,negated_conjecture,
( ( ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) )
& ( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| ( in(esk1_0,esk3_0)
& in(esk2_0,esk4_0) ) ) ),
inference(skolemize,[status(esa)],[19]) ).
fof(21,negated_conjecture,
( ( ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) )
& ( in(esk1_0,esk3_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) )
& ( in(esk2_0,esk4_0)
| in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(22,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| in(esk2_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(23,negated_conjecture,
( in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0))
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(24,negated_conjecture,
( ~ in(esk2_0,esk4_0)
| ~ in(esk1_0,esk3_0)
| ~ in(ordered_pair(esk1_0,esk2_0),cartesian_product2(esk3_0,esk4_0)) ),
inference(split_conjunct,[status(thm)],[21]) ).
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(32,plain,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) != ordered_pair(X3,X4)
| ( X1 = X3
& X2 = X4 ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(33,plain,
! [X5,X6,X7,X8] :
( ordered_pair(X5,X6) != ordered_pair(X7,X8)
| ( X5 = X7
& X6 = X8 ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X5,X6,X7,X8] :
( ( X5 = X7
| ordered_pair(X5,X6) != ordered_pair(X7,X8) )
& ( X6 = X8
| ordered_pair(X5,X6) != ordered_pair(X7,X8) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(35,plain,
( X2 = X4
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,plain,
( X1 = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(42,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[9]) ).
cnf(43,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[42]) ).
fof(49,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)],[13]) ).
fof(50,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)],[49]) ).
fof(51,plain,
! [X7,X8,X9] :
( ( X9 != cartesian_product2(X7,X8)
| ! [X10] :
( ( ~ in(X10,X9)
| ( in(esk7_4(X7,X8,X9,X10),X7)
& in(esk8_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk7_4(X7,X8,X9,X10),esk8_4(X7,X8,X9,X10)) ) )
& ( ! [X13,X14] :
( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14) )
| in(X10,X9) ) ) )
& ( ( ( ~ in(esk9_3(X7,X8,X9),X9)
| ! [X16,X17] :
( ~ in(X16,X7)
| ~ in(X17,X8)
| esk9_3(X7,X8,X9) != ordered_pair(X16,X17) ) )
& ( in(esk9_3(X7,X8,X9),X9)
| ( in(esk10_3(X7,X8,X9),X7)
& in(esk11_3(X7,X8,X9),X8)
& esk9_3(X7,X8,X9) = ordered_pair(esk10_3(X7,X8,X9),esk11_3(X7,X8,X9)) ) ) )
| X9 = cartesian_product2(X7,X8) ) ),
inference(skolemize,[status(esa)],[50]) ).
fof(52,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk9_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk9_3(X7,X8,X9),X9) )
& ( in(esk9_3(X7,X8,X9),X9)
| ( in(esk10_3(X7,X8,X9),X7)
& in(esk11_3(X7,X8,X9),X8)
& esk9_3(X7,X8,X9) = ordered_pair(esk10_3(X7,X8,X9),esk11_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(esk7_4(X7,X8,X9,X10),X7)
& in(esk8_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk7_4(X7,X8,X9,X10),esk8_4(X7,X8,X9,X10)) ) ) )
| X9 != cartesian_product2(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[51]) ).
fof(53,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk9_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk9_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk10_3(X7,X8,X9),X7)
| in(esk9_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk11_3(X7,X8,X9),X8)
| in(esk9_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( esk9_3(X7,X8,X9) = ordered_pair(esk10_3(X7,X8,X9),esk11_3(X7,X8,X9))
| in(esk9_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(esk7_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk8_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk7_4(X7,X8,X9,X10),esk8_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) ) ),
inference(distribute,[status(thm)],[52]) ).
cnf(54,plain,
( X4 = ordered_pair(esk7_4(X2,X3,X1,X4),esk8_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,plain,
( in(esk8_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,plain,
( in(esk7_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(57,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(62,negated_conjecture,
( in(esk1_0,esk3_0)
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[23,27,theory(equality)]),
[unfolding] ).
cnf(63,negated_conjecture,
( in(esk2_0,esk4_0)
| in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[22,27,theory(equality)]),
[unfolding] ).
cnf(65,plain,
( X2 = X4
| unordered_pair(unordered_pair(X1,X2),singleton(X1)) != unordered_pair(unordered_pair(X3,X4),singleton(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[35,27,theory(equality)]),27,theory(equality)]),
[unfolding] ).
cnf(66,plain,
( X1 = X3
| unordered_pair(unordered_pair(X1,X2),singleton(X1)) != unordered_pair(unordered_pair(X3,X4),singleton(X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[36,27,theory(equality)]),27,theory(equality)]),
[unfolding] ).
cnf(67,plain,
( unordered_pair(unordered_pair(esk7_4(X2,X3,X1,X4),esk8_4(X2,X3,X1,X4)),singleton(esk7_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[54,27,theory(equality)]),
[unfolding] ).
cnf(68,plain,
( in(X4,X1)
| unordered_pair(unordered_pair(X5,X6),singleton(X5)) != X4
| cartesian_product2(X2,X3) != X1
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(rw,[status(thm)],[57,27,theory(equality)]),
[unfolding] ).
cnf(71,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0)
| ~ in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,esk4_0)) ),
inference(rw,[status(thm)],[24,27,theory(equality)]),
[unfolding] ).
cnf(76,plain,
( X1 = X2
| unordered_pair(singleton(X3),unordered_pair(X3,X1)) != unordered_pair(unordered_pair(X4,X2),singleton(X4)) ),
inference(spm,[status(thm)],[65,43,theory(equality)]) ).
cnf(89,plain,
( X1 = X2
| unordered_pair(singleton(X1),unordered_pair(X1,X3)) != unordered_pair(unordered_pair(X2,X4),singleton(X2)) ),
inference(spm,[status(thm)],[66,43,theory(equality)]) ).
cnf(102,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| cartesian_product2(X4,X5) != X3
| ~ in(X2,X5)
| ~ in(X1,X4) ),
inference(er,[status(thm)],[68,theory(equality)]) ).
cnf(111,plain,
( unordered_pair(singleton(esk7_4(X2,X3,X1,X4)),unordered_pair(esk7_4(X2,X3,X1,X4),esk8_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[67,43,theory(equality)]) ).
cnf(163,plain,
( esk8_4(X1,X2,X3,X4) = X5
| X4 != unordered_pair(unordered_pair(X6,X5),singleton(X6))
| cartesian_product2(X1,X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[76,111,theory(equality)]) ).
cnf(200,plain,
( esk7_4(X1,X2,X3,X4) = X5
| X4 != unordered_pair(unordered_pair(X5,X6),singleton(X5))
| cartesian_product2(X1,X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[89,111,theory(equality)]) ).
cnf(216,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[102,theory(equality)]) ).
cnf(222,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| ~ in(esk2_0,esk4_0) ),
inference(spm,[status(thm)],[71,216,theory(equality)]) ).
cnf(579,plain,
( esk8_4(X1,X2,X3,unordered_pair(unordered_pair(X4,X5),singleton(X4))) = X5
| cartesian_product2(X1,X2) != X3
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(er,[status(thm)],[163,theory(equality)]) ).
cnf(653,plain,
( esk7_4(X1,X2,X3,unordered_pair(unordered_pair(X4,X5),singleton(X4))) = X4
| cartesian_product2(X1,X2) != X3
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(er,[status(thm)],[200,theory(equality)]) ).
cnf(732,plain,
( in(X5,X2)
| cartesian_product2(X1,X2) != X3
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(spm,[status(thm)],[55,579,theory(equality)]) ).
cnf(757,negated_conjecture,
( in(esk2_0,X1)
| in(esk2_0,esk4_0)
| cartesian_product2(X2,X1) != cartesian_product2(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[732,63,theory(equality)]) ).
cnf(776,negated_conjecture,
in(esk2_0,esk4_0),
inference(er,[status(thm)],[757,theory(equality)]) ).
cnf(780,negated_conjecture,
( ~ in(esk1_0,esk3_0)
| $false ),
inference(rw,[status(thm)],[222,776,theory(equality)]) ).
cnf(781,negated_conjecture,
~ in(esk1_0,esk3_0),
inference(cn,[status(thm)],[780,theory(equality)]) ).
cnf(792,negated_conjecture,
in(unordered_pair(unordered_pair(esk1_0,esk2_0),singleton(esk1_0)),cartesian_product2(esk3_0,esk4_0)),
inference(sr,[status(thm)],[62,781,theory(equality)]) ).
cnf(2241,plain,
( in(X4,X1)
| cartesian_product2(X1,X2) != X3
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X3) ),
inference(spm,[status(thm)],[56,653,theory(equality)]) ).
cnf(2294,negated_conjecture,
( in(esk1_0,X1)
| cartesian_product2(X1,X2) != cartesian_product2(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[2241,792,theory(equality)]) ).
cnf(2303,negated_conjecture,
in(esk1_0,esk3_0),
inference(er,[status(thm)],[2294,theory(equality)]) ).
cnf(2304,negated_conjecture,
$false,
inference(sr,[status(thm)],[2303,781,theory(equality)]) ).
cnf(2305,negated_conjecture,
$false,
2304,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU157+1.p
% --creating new selector for []
% -running prover on /tmp/tmpX9Gq5w/sel_SEU157+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU157+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU157+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU157+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
%
%------------------------------------------------------------------------------