TSTP Solution File: SEU166+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU166+1 : TPTP v5.0.0. Released v3.3.0.
% 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 : Sun Dec 26 05:00:02 EST 2010
% Result : Theorem 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 13 unt; 0 def)
% Number of atoms : 251 ( 64 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 324 ( 130 ~; 136 |; 52 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 193 ( 0 sgn 76 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpowiWD5/sel_SEU166+1.p_1',d5_tarski) ).
fof(7,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpowiWD5/sel_SEU166+1.p_1',commutativity_k2_tarski) ).
fof(9,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('/tmp/tmpowiWD5/sel_SEU166+1.p_1',t118_zfmisc_1) ).
fof(12,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpowiWD5/sel_SEU166+1.p_1',d3_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/tmpowiWD5/sel_SEU166+1.p_1',d2_zfmisc_1) ).
fof(15,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(20,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[2]) ).
cnf(21,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[20]) ).
fof(31,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(32,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[31]) ).
fof(34,negated_conjecture,
? [X1,X2,X3] :
( subset(X1,X2)
& ( ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(35,negated_conjecture,
? [X4,X5,X6] :
( subset(X4,X5)
& ( ~ subset(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
| ~ subset(cartesian_product2(X6,X4),cartesian_product2(X6,X5)) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( subset(esk3_0,esk4_0)
& ( ~ subset(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk4_0,esk5_0))
| ~ subset(cartesian_product2(esk5_0,esk3_0),cartesian_product2(esk5_0,esk4_0)) ) ),
inference(skolemize,[status(esa)],[35]) ).
cnf(37,negated_conjecture,
( ~ subset(cartesian_product2(esk5_0,esk3_0),cartesian_product2(esk5_0,esk4_0))
| ~ subset(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk4_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[36]) ).
fof(43,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(44,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[43]) ).
fof(45,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk6_2(X4,X5),X4)
& ~ in(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[44]) ).
fof(46,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk6_2(X4,X5),X4)
& ~ in(esk6_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[45]) ).
fof(47,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk6_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk6_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(48,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(49,plain,
( subset(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
cnf(50,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(51,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(52,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)],[51]) ).
fof(53,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)],[52]) ).
fof(54,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)],[53]) ).
fof(55,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)],[54]) ).
cnf(56,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)],[55]) ).
cnf(57,plain,
( in(esk8_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(58,plain,
( in(esk7_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
cnf(59,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)],[55]) ).
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)],[56,21,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)],[59,21,theory(equality)]),
[unfolding] ).
cnf(74,negated_conjecture,
( in(X1,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[50,38,theory(equality)]) ).
cnf(86,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(96,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)],[67,32,theory(equality)]) ).
cnf(129,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[86,theory(equality)]) ).
cnf(131,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[129,32,theory(equality)]) ).
cnf(152,plain,
( in(X4,cartesian_product2(X5,X6))
| ~ in(esk8_4(X1,X2,X3,X4),X6)
| ~ in(esk7_4(X1,X2,X3,X4),X5)
| cartesian_product2(X1,X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[131,96,theory(equality)]) ).
cnf(264,plain,
( in(X1,cartesian_product2(X2,X3))
| cartesian_product2(X4,X3) != X5
| ~ in(esk7_4(X4,X3,X5,X1),X2)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[152,57,theory(equality)]) ).
cnf(265,negated_conjecture,
( in(X1,cartesian_product2(X2,esk4_0))
| cartesian_product2(X3,X4) != X5
| ~ in(esk7_4(X3,X4,X5,X1),X2)
| ~ in(X1,X5)
| ~ in(esk8_4(X3,X4,X5,X1),esk3_0) ),
inference(spm,[status(thm)],[152,74,theory(equality)]) ).
cnf(267,negated_conjecture,
( in(X1,cartesian_product2(esk4_0,X2))
| cartesian_product2(X3,X2) != X4
| ~ in(X1,X4)
| ~ in(esk7_4(X3,X2,X4,X1),esk3_0) ),
inference(spm,[status(thm)],[264,74,theory(equality)]) ).
cnf(270,negated_conjecture,
( in(X1,cartesian_product2(esk4_0,X2))
| cartesian_product2(esk3_0,X2) != X3
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[267,58,theory(equality)]) ).
cnf(271,negated_conjecture,
( in(X1,cartesian_product2(esk4_0,X2))
| ~ in(X1,cartesian_product2(esk3_0,X2)) ),
inference(er,[status(thm)],[270,theory(equality)]) ).
cnf(272,negated_conjecture,
( subset(X1,cartesian_product2(esk4_0,X2))
| ~ in(esk6_2(X1,cartesian_product2(esk4_0,X2)),cartesian_product2(esk3_0,X2)) ),
inference(spm,[status(thm)],[48,271,theory(equality)]) ).
cnf(291,negated_conjecture,
subset(cartesian_product2(esk3_0,X1),cartesian_product2(esk4_0,X1)),
inference(spm,[status(thm)],[272,49,theory(equality)]) ).
cnf(293,negated_conjecture,
( $false
| ~ subset(cartesian_product2(esk5_0,esk3_0),cartesian_product2(esk5_0,esk4_0)) ),
inference(rw,[status(thm)],[37,291,theory(equality)]) ).
cnf(294,negated_conjecture,
~ subset(cartesian_product2(esk5_0,esk3_0),cartesian_product2(esk5_0,esk4_0)),
inference(cn,[status(thm)],[293,theory(equality)]) ).
cnf(397,negated_conjecture,
( in(X1,cartesian_product2(X2,esk4_0))
| cartesian_product2(X3,esk3_0) != X4
| ~ in(esk7_4(X3,esk3_0,X4,X1),X2)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[265,57,theory(equality)]) ).
cnf(398,negated_conjecture,
( in(X1,cartesian_product2(X2,esk4_0))
| cartesian_product2(X2,esk3_0) != X3
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[397,58,theory(equality)]) ).
cnf(404,negated_conjecture,
( in(X1,cartesian_product2(X2,esk4_0))
| ~ in(X1,cartesian_product2(X2,esk3_0)) ),
inference(er,[status(thm)],[398,theory(equality)]) ).
cnf(405,negated_conjecture,
( subset(X1,cartesian_product2(X2,esk4_0))
| ~ in(esk6_2(X1,cartesian_product2(X2,esk4_0)),cartesian_product2(X2,esk3_0)) ),
inference(spm,[status(thm)],[48,404,theory(equality)]) ).
cnf(492,negated_conjecture,
subset(cartesian_product2(X1,esk3_0),cartesian_product2(X1,esk4_0)),
inference(spm,[status(thm)],[405,49,theory(equality)]) ).
cnf(498,negated_conjecture,
$false,
inference(rw,[status(thm)],[294,492,theory(equality)]) ).
cnf(499,negated_conjecture,
$false,
inference(cn,[status(thm)],[498,theory(equality)]) ).
cnf(500,negated_conjecture,
$false,
499,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU166+1.p
% --creating new selector for []
% -running prover on /tmp/tmpowiWD5/sel_SEU166+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU166+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU166+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU166+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
%
%------------------------------------------------------------------------------