TSTP Solution File: SEU166+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU166+3 : TPTP v5.0.0. Released v3.2.0.
% 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 05:04:57 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% 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(1,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpCua8pH/sel_SEU166+3.p_1',d5_tarski) ).
fof(2,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/tmpCua8pH/sel_SEU166+3.p_1',d2_zfmisc_1) ).
fof(5,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpCua8pH/sel_SEU166+3.p_1',commutativity_k2_tarski) ).
fof(6,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/tmpCua8pH/sel_SEU166+3.p_1',t118_zfmisc_1) ).
fof(9,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpCua8pH/sel_SEU166+3.p_1',d3_tarski) ).
fof(11,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)],[6]) ).
fof(15,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(16,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,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)],[2]) ).
fof(18,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)],[17]) ).
fof(19,plain,
! [X7,X8,X9] :
( ( X9 != cartesian_product2(X7,X8)
| ! [X10] :
( ( ~ in(X10,X9)
| ( in(esk1_4(X7,X8,X9,X10),X7)
& in(esk2_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10)) ) )
& ( ! [X13,X14] :
( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14) )
| in(X10,X9) ) ) )
& ( ( ( ~ in(esk3_3(X7,X8,X9),X9)
| ! [X16,X17] :
( ~ in(X16,X7)
| ~ in(X17,X8)
| esk3_3(X7,X8,X9) != ordered_pair(X16,X17) ) )
& ( in(esk3_3(X7,X8,X9),X9)
| ( in(esk4_3(X7,X8,X9),X7)
& in(esk5_3(X7,X8,X9),X8)
& esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9)) ) ) )
| X9 = cartesian_product2(X7,X8) ) ),
inference(skolemize,[status(esa)],[18]) ).
fof(20,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk3_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk3_3(X7,X8,X9),X9) )
& ( in(esk3_3(X7,X8,X9),X9)
| ( in(esk4_3(X7,X8,X9),X7)
& in(esk5_3(X7,X8,X9),X8)
& esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_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(esk1_4(X7,X8,X9,X10),X7)
& in(esk2_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10)) ) ) )
| X9 != cartesian_product2(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[19]) ).
fof(21,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk3_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk3_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk4_3(X7,X8,X9),X7)
| in(esk3_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk5_3(X7,X8,X9),X8)
| in(esk3_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9))
| in(esk3_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(esk1_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk2_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(22,plain,
( X4 = ordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(23,plain,
( in(esk2_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(24,plain,
( in(esk1_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(25,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)],[21]) ).
fof(35,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(36,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,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)],[11]) ).
fof(38,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)],[37]) ).
fof(39,negated_conjecture,
( subset(esk7_0,esk8_0)
& ( ~ subset(cartesian_product2(esk7_0,esk9_0),cartesian_product2(esk8_0,esk9_0))
| ~ subset(cartesian_product2(esk9_0,esk7_0),cartesian_product2(esk9_0,esk8_0)) ) ),
inference(skolemize,[status(esa)],[38]) ).
cnf(40,negated_conjecture,
( ~ subset(cartesian_product2(esk9_0,esk7_0),cartesian_product2(esk9_0,esk8_0))
| ~ subset(cartesian_product2(esk7_0,esk9_0),cartesian_product2(esk8_0,esk9_0)) ),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(41,negated_conjecture,
subset(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[39]) ).
fof(48,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)],[9]) ).
fof(49,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)],[48]) ).
fof(50,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk11_2(X4,X5),X4)
& ~ in(esk11_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[49]) ).
fof(51,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk11_2(X4,X5),X4)
& ~ in(esk11_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[50]) ).
fof(52,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk11_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk11_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[51]) ).
cnf(53,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(54,plain,
( subset(X1,X2)
| in(esk11_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(55,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
cnf(59,plain,
( unordered_pair(unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4)),singleton(esk1_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[22,16,theory(equality)]),
[unfolding] ).
cnf(60,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)],[25,16,theory(equality)]),
[unfolding] ).
cnf(66,negated_conjecture,
( in(X1,esk8_0)
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[55,41,theory(equality)]) ).
cnf(78,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)],[60,theory(equality)]) ).
cnf(88,plain,
( unordered_pair(singleton(esk1_4(X2,X3,X1,X4)),unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[59,36,theory(equality)]) ).
cnf(121,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[78,theory(equality)]) ).
cnf(123,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[121,36,theory(equality)]) ).
cnf(144,plain,
( in(X4,cartesian_product2(X5,X6))
| ~ in(esk2_4(X1,X2,X3,X4),X6)
| ~ in(esk1_4(X1,X2,X3,X4),X5)
| cartesian_product2(X1,X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[123,88,theory(equality)]) ).
cnf(256,plain,
( in(X1,cartesian_product2(X2,X3))
| cartesian_product2(X4,X3) != X5
| ~ in(esk1_4(X4,X3,X5,X1),X2)
| ~ in(X1,X5) ),
inference(spm,[status(thm)],[144,23,theory(equality)]) ).
cnf(257,negated_conjecture,
( in(X1,cartesian_product2(X2,esk8_0))
| cartesian_product2(X3,X4) != X5
| ~ in(esk1_4(X3,X4,X5,X1),X2)
| ~ in(X1,X5)
| ~ in(esk2_4(X3,X4,X5,X1),esk7_0) ),
inference(spm,[status(thm)],[144,66,theory(equality)]) ).
cnf(259,negated_conjecture,
( in(X1,cartesian_product2(esk8_0,X2))
| cartesian_product2(X3,X2) != X4
| ~ in(X1,X4)
| ~ in(esk1_4(X3,X2,X4,X1),esk7_0) ),
inference(spm,[status(thm)],[256,66,theory(equality)]) ).
cnf(262,negated_conjecture,
( in(X1,cartesian_product2(esk8_0,X2))
| cartesian_product2(esk7_0,X2) != X3
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[259,24,theory(equality)]) ).
cnf(263,negated_conjecture,
( in(X1,cartesian_product2(esk8_0,X2))
| ~ in(X1,cartesian_product2(esk7_0,X2)) ),
inference(er,[status(thm)],[262,theory(equality)]) ).
cnf(264,negated_conjecture,
( subset(X1,cartesian_product2(esk8_0,X2))
| ~ in(esk11_2(X1,cartesian_product2(esk8_0,X2)),cartesian_product2(esk7_0,X2)) ),
inference(spm,[status(thm)],[53,263,theory(equality)]) ).
cnf(283,negated_conjecture,
subset(cartesian_product2(esk7_0,X1),cartesian_product2(esk8_0,X1)),
inference(spm,[status(thm)],[264,54,theory(equality)]) ).
cnf(285,negated_conjecture,
( $false
| ~ subset(cartesian_product2(esk9_0,esk7_0),cartesian_product2(esk9_0,esk8_0)) ),
inference(rw,[status(thm)],[40,283,theory(equality)]) ).
cnf(286,negated_conjecture,
~ subset(cartesian_product2(esk9_0,esk7_0),cartesian_product2(esk9_0,esk8_0)),
inference(cn,[status(thm)],[285,theory(equality)]) ).
cnf(389,negated_conjecture,
( in(X1,cartesian_product2(X2,esk8_0))
| cartesian_product2(X3,esk7_0) != X4
| ~ in(esk1_4(X3,esk7_0,X4,X1),X2)
| ~ in(X1,X4) ),
inference(spm,[status(thm)],[257,23,theory(equality)]) ).
cnf(390,negated_conjecture,
( in(X1,cartesian_product2(X2,esk8_0))
| cartesian_product2(X2,esk7_0) != X3
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[389,24,theory(equality)]) ).
cnf(396,negated_conjecture,
( in(X1,cartesian_product2(X2,esk8_0))
| ~ in(X1,cartesian_product2(X2,esk7_0)) ),
inference(er,[status(thm)],[390,theory(equality)]) ).
cnf(397,negated_conjecture,
( subset(X1,cartesian_product2(X2,esk8_0))
| ~ in(esk11_2(X1,cartesian_product2(X2,esk8_0)),cartesian_product2(X2,esk7_0)) ),
inference(spm,[status(thm)],[53,396,theory(equality)]) ).
cnf(484,negated_conjecture,
subset(cartesian_product2(X1,esk7_0),cartesian_product2(X1,esk8_0)),
inference(spm,[status(thm)],[397,54,theory(equality)]) ).
cnf(490,negated_conjecture,
$false,
inference(rw,[status(thm)],[286,484,theory(equality)]) ).
cnf(491,negated_conjecture,
$false,
inference(cn,[status(thm)],[490,theory(equality)]) ).
cnf(492,negated_conjecture,
$false,
491,
[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/SEU166+3.p
% --creating new selector for []
% -running prover on /tmp/tmpCua8pH/sel_SEU166+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU166+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU166+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU166+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
%
%------------------------------------------------------------------------------