TSTP Solution File: SEU187+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU187+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 05:17:33 EST 2010
% Result : Theorem 0.46s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 24 unt; 0 def)
% Number of atoms : 216 ( 73 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 249 ( 93 ~; 116 |; 33 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-3 aty)
% Number of variables : 124 ( 2 sgn 76 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',d5_relat_1) ).
fof(43,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',t69_enumset1) ).
fof(77,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',t1_boole) ).
fof(92,axiom,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',t46_zfmisc_1) ).
fof(94,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',commutativity_k2_tarski) ).
fof(96,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',fc4_relat_1) ).
fof(105,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',d4_relat_1) ).
fof(116,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',d5_tarski) ).
fof(141,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',t60_relat_1) ).
fof(147,axiom,
! [X1] : singleton(X1) != empty_set,
file('/tmp/tmpgFFgHY/sel_SEU187+2.p_1',l1_zfmisc_1) ).
fof(168,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(assume_negation,[status(cth)],[141]) ).
fof(195,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_rng(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) )
& ( ! [X4] : ~ in(ordered_pair(X4,X3),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X4,X3),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X4,X3),X1) ) )
| X2 = relation_rng(X1) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(196,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X8,X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X11,X10),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X12,X10),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(variable_rename,[status(thm)],[195]) ).
fof(197,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_rng(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) )
& ( ! [X9] : ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk2_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) ) ) ),
inference(skolemize,[status(esa)],[196]) ).
fof(198,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5) ) )
| X6 = relation_rng(X5) )
& ( ( ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5) ) )
| X6 != relation_rng(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[197]) ).
fof(199,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(X11,esk2_2(X5,X6)),X5)
| ~ in(esk2_2(X5,X6),X6)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( in(esk2_2(X5,X6),X6)
| in(ordered_pair(esk3_2(X5,X6),esk2_2(X5,X6)),X5)
| X6 = relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X9,X7),X5)
| in(X7,X6)
| X6 != relation_rng(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(esk1_3(X5,X6,X7),X7),X5)
| X6 != relation_rng(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[198]) ).
cnf(202,plain,
( X2 = relation_rng(X1)
| in(ordered_pair(esk3_2(X1,X2),esk2_2(X1,X2)),X1)
| in(esk2_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[199]) ).
fof(346,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[43]) ).
cnf(347,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[346]) ).
fof(501,plain,
! [X2] : set_union2(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[77]) ).
cnf(502,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[501]) ).
fof(548,plain,
! [X1,X2] :
( ~ in(X1,X2)
| set_union2(singleton(X1),X2) = X2 ),
inference(fof_nnf,[status(thm)],[92]) ).
fof(549,plain,
! [X3,X4] :
( ~ in(X3,X4)
| set_union2(singleton(X3),X4) = X4 ),
inference(variable_rename,[status(thm)],[548]) ).
cnf(550,plain,
( set_union2(singleton(X1),X2) = X2
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[549]) ).
fof(557,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[94]) ).
cnf(558,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[557]) ).
cnf(563,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[96]) ).
fof(594,plain,
! [X1] :
( ~ relation(X1)
| ! [X2] :
( ( X2 != relation_dom(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) )
& ( ! [X4] : ~ in(ordered_pair(X3,X4),X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] : ~ in(ordered_pair(X3,X4),X1) )
& ( in(X3,X2)
| ? [X4] : in(ordered_pair(X3,X4),X1) ) )
| X2 = relation_dom(X1) ) ) ),
inference(fof_nnf,[status(thm)],[105]) ).
fof(595,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] : in(ordered_pair(X7,X8),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] : ~ in(ordered_pair(X10,X11),X5) )
& ( in(X10,X6)
| ? [X12] : in(ordered_pair(X10,X12),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(variable_rename,[status(thm)],[594]) ).
fof(596,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk30_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk31_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk31_2(X5,X6),X11),X5) )
& ( in(esk31_2(X5,X6),X6)
| in(ordered_pair(esk31_2(X5,X6),esk32_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(skolemize,[status(esa)],[595]) ).
fof(597,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk31_2(X5,X6),X11),X5)
| ~ in(esk31_2(X5,X6),X6) )
& ( in(esk31_2(X5,X6),X6)
| in(ordered_pair(esk31_2(X5,X6),esk32_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk30_3(X5,X6,X7)),X5) ) )
| X6 != relation_dom(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[596]) ).
fof(598,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk31_2(X5,X6),X11),X5)
| ~ in(esk31_2(X5,X6),X6)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk31_2(X5,X6),X6)
| in(ordered_pair(esk31_2(X5,X6),esk32_2(X5,X6)),X5)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6)
| X6 != relation_dom(X5)
| ~ relation(X5) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk30_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[597]) ).
cnf(601,plain,
( X2 = relation_dom(X1)
| in(ordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),X1)
| in(esk31_2(X1,X2),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[598]) ).
fof(633,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[116]) ).
cnf(634,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[633]) ).
fof(725,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(fof_nnf,[status(thm)],[168]) ).
cnf(726,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(split_conjunct,[status(thm)],[725]) ).
fof(742,plain,
! [X2] : singleton(X2) != empty_set,
inference(variable_rename,[status(thm)],[147]) ).
cnf(743,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[742]) ).
cnf(842,plain,
unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[634,347,theory(equality)]),
[unfolding] ).
cnf(853,plain,
( set_union2(unordered_pair(X1,X1),X2) = X2
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[550,347,theory(equality)]),
[unfolding] ).
cnf(865,plain,
unordered_pair(X1,X1) != empty_set,
inference(rw,[status(thm)],[743,347,theory(equality)]),
[unfolding] ).
cnf(895,plain,
( relation_rng(X1) = X2
| in(esk2_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk3_2(X1,X2),esk2_2(X1,X2)),unordered_pair(esk3_2(X1,X2),esk3_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[202,842,theory(equality)]),
[unfolding] ).
cnf(896,plain,
( relation_dom(X1) = X2
| in(esk31_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk31_2(X1,X2),esk32_2(X1,X2)),unordered_pair(esk31_2(X1,X2),esk31_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[601,842,theory(equality)]),
[unfolding] ).
cnf(1172,plain,
( empty_set = unordered_pair(X1,X1)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[502,853,theory(equality)]) ).
cnf(1182,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[1172,865,theory(equality)]) ).
cnf(3361,plain,
( relation_rng(X1) = X2
| in(esk2_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),unordered_pair(esk3_2(X1,X2),esk3_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[895,558,theory(equality)]) ).
cnf(3454,plain,
( relation_dom(X1) = X2
| in(esk31_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk31_2(X1,X2),esk31_2(X1,X2)),unordered_pair(esk31_2(X1,X2),esk32_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[896,558,theory(equality)]) ).
cnf(3819,plain,
( relation_rng(empty_set) = X1
| in(esk2_2(empty_set,X1),X1)
| ~ relation(empty_set) ),
inference(spm,[status(thm)],[1182,3361,theory(equality)]) ).
cnf(3820,plain,
( relation_dom(empty_set) = X1
| in(esk31_2(empty_set,X1),X1)
| ~ relation(empty_set) ),
inference(spm,[status(thm)],[1182,3454,theory(equality)]) ).
cnf(3840,plain,
( relation_rng(empty_set) = X1
| in(esk2_2(empty_set,X1),X1)
| $false ),
inference(rw,[status(thm)],[3819,563,theory(equality)]) ).
cnf(3841,plain,
( relation_rng(empty_set) = X1
| in(esk2_2(empty_set,X1),X1) ),
inference(cn,[status(thm)],[3840,theory(equality)]) ).
cnf(3842,plain,
( relation_dom(empty_set) = X1
| in(esk31_2(empty_set,X1),X1)
| $false ),
inference(rw,[status(thm)],[3820,563,theory(equality)]) ).
cnf(3843,plain,
( relation_dom(empty_set) = X1
| in(esk31_2(empty_set,X1),X1) ),
inference(cn,[status(thm)],[3842,theory(equality)]) ).
cnf(4160,plain,
relation_rng(empty_set) = empty_set,
inference(spm,[status(thm)],[1182,3841,theory(equality)]) ).
cnf(4181,negated_conjecture,
( $false
| relation_dom(empty_set) != empty_set ),
inference(rw,[status(thm)],[726,4160,theory(equality)]) ).
cnf(4182,negated_conjecture,
relation_dom(empty_set) != empty_set,
inference(cn,[status(thm)],[4181,theory(equality)]) ).
cnf(4218,plain,
relation_dom(empty_set) = empty_set,
inference(spm,[status(thm)],[1182,3843,theory(equality)]) ).
cnf(4232,plain,
$false,
inference(sr,[status(thm)],[4218,4182,theory(equality)]) ).
cnf(4233,plain,
$false,
4232,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU187+2.p
% --creating new selector for []
% -running prover on /tmp/tmpgFFgHY/sel_SEU187+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU187+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU187+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU187+2.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
%
%------------------------------------------------------------------------------