TSTP Solution File: SEU187+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU187+1 : 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 05:17:28 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 16 unt; 0 def)
% Number of atoms : 246 ( 61 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 302 ( 123 ~; 136 |; 34 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-3 aty)
% Number of variables : 145 ( 3 sgn 85 !; 16 ?)
% 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/tmpp2tEnq/sel_SEU187+1.p_1',d5_relat_1) ).
fof(6,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',t7_boole) ).
fof(10,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',commutativity_k2_tarski) ).
fof(11,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',t60_relat_1) ).
fof(12,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',fc4_relat_1) ).
fof(15,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',cc1_relat_1) ).
fof(17,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',d4_relat_1) ).
fof(18,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',t2_subset) ).
fof(25,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',d5_tarski) ).
fof(26,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',t6_boole) ).
fof(27,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/tmp/tmpp2tEnq/sel_SEU187+1.p_1',existence_m1_subset_1) ).
fof(33,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(assume_negation,[status(cth)],[11]) ).
fof(42,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(43,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)],[42]) ).
fof(44,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)],[43]) ).
fof(45,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)],[44]) ).
fof(46,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)],[45]) ).
cnf(49,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)],[46]) ).
fof(64,plain,
! [X1,X2] :
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(65,plain,
! [X3,X4] :
( ~ in(X3,X4)
| ~ empty(X4) ),
inference(variable_rename,[status(thm)],[64]) ).
cnf(66,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(77,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[10]) ).
cnf(78,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[77]) ).
fof(79,negated_conjecture,
( relation_dom(empty_set) != empty_set
| relation_rng(empty_set) != empty_set ),
inference(fof_nnf,[status(thm)],[33]) ).
cnf(80,negated_conjecture,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(split_conjunct,[status(thm)],[79]) ).
cnf(82,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[12]) ).
fof(87,plain,
! [X1] :
( ~ empty(X1)
| relation(X1) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(88,plain,
! [X2] :
( ~ empty(X2)
| relation(X2) ),
inference(variable_rename,[status(thm)],[87]) ).
cnf(89,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[88]) ).
fof(91,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)],[17]) ).
fof(92,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)],[91]) ).
fof(93,plain,
! [X5] :
( ~ relation(X5)
| ! [X6] :
( ( X6 != relation_dom(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| in(ordered_pair(X7,esk7_3(X5,X6,X7)),X5) )
& ( ! [X9] : ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk8_2(X5,X6),X6)
| ! [X11] : ~ in(ordered_pair(esk8_2(X5,X6),X11),X5) )
& ( in(esk8_2(X5,X6),X6)
| in(ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) ) ) ),
inference(skolemize,[status(esa)],[92]) ).
fof(94,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ( ~ in(ordered_pair(esk8_2(X5,X6),X11),X5)
| ~ in(esk8_2(X5,X6),X6) )
& ( in(esk8_2(X5,X6),X6)
| in(ordered_pair(esk8_2(X5,X6),esk9_2(X5,X6)),X5) ) )
| X6 = relation_dom(X5) )
& ( ( ( ~ in(ordered_pair(X7,X9),X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| in(ordered_pair(X7,esk7_3(X5,X6,X7)),X5) ) )
| X6 != relation_dom(X5) ) )
| ~ relation(X5) ),
inference(shift_quantors,[status(thm)],[93]) ).
fof(95,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(ordered_pair(esk8_2(X5,X6),X11),X5)
| ~ in(esk8_2(X5,X6),X6)
| X6 = relation_dom(X5)
| ~ relation(X5) )
& ( in(esk8_2(X5,X6),X6)
| in(ordered_pair(esk8_2(X5,X6),esk9_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,esk7_3(X5,X6,X7)),X5)
| X6 != relation_dom(X5)
| ~ relation(X5) ) ),
inference(distribute,[status(thm)],[94]) ).
cnf(96,plain,
( in(ordered_pair(X3,esk7_3(X1,X2,X3)),X1)
| ~ relation(X1)
| X2 != relation_dom(X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[95]) ).
fof(100,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(101,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[100]) ).
cnf(102,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(112,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[25]) ).
cnf(113,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[112]) ).
fof(114,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(115,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[114]) ).
cnf(116,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[115]) ).
fof(117,plain,
! [X3] :
? [X4] : element(X4,X3),
inference(variable_rename,[status(thm)],[27]) ).
fof(118,plain,
! [X3] : element(esk10_1(X3),X3),
inference(skolemize,[status(esa)],[117]) ).
cnf(119,plain,
element(esk10_1(X1),X1),
inference(split_conjunct,[status(thm)],[118]) ).
cnf(132,plain,
( relation_rng(X1) = X2
| in(esk2_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk3_2(X1,X2),esk2_2(X1,X2)),singleton(esk3_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[49,113,theory(equality)]),
[unfolding] ).
cnf(136,plain,
( in(unordered_pair(unordered_pair(X3,esk7_3(X1,X2,X3)),singleton(X3)),X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(rw,[status(thm)],[96,113,theory(equality)]),
[unfolding] ).
cnf(149,plain,
( empty(X1)
| in(esk10_1(X1),X1) ),
inference(spm,[status(thm)],[102,119,theory(equality)]) ).
cnf(166,plain,
( in(unordered_pair(singleton(X3),unordered_pair(X3,esk7_3(X1,X2,X3))),X1)
| relation_dom(X1) != X2
| ~ relation(X1)
| ~ in(X3,X2) ),
inference(rw,[status(thm)],[136,78,theory(equality)]) ).
cnf(167,plain,
( ~ empty(X1)
| relation_dom(X1) != X3
| ~ in(X2,X3)
| ~ relation(X1) ),
inference(spm,[status(thm)],[66,166,theory(equality)]) ).
cnf(181,plain,
( relation_rng(X1) = X2
| in(esk2_2(X1,X2),X2)
| in(unordered_pair(singleton(esk3_2(X1,X2)),unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[132,78,theory(equality)]),78,theory(equality)]) ).
cnf(182,plain,
( relation_rng(X1) = X2
| in(esk2_2(X1,X2),X2)
| ~ empty(X1)
| ~ relation(X1) ),
inference(spm,[status(thm)],[66,181,theory(equality)]) ).
cnf(201,plain,
( relation_rng(X1) = X2
| in(esk2_2(X1,X2),X2)
| ~ empty(X1) ),
inference(csr,[status(thm)],[182,89]) ).
cnf(202,plain,
( relation_rng(X2) = X1
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[66,201,theory(equality)]) ).
cnf(204,plain,
( relation_rng(X1) = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[202,82,theory(equality)]) ).
cnf(208,plain,
( relation_dom(X1) != X3
| ~ empty(X1)
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[167,89]) ).
cnf(216,plain,
( empty(X2)
| relation_dom(X1) != X2
| ~ empty(X1) ),
inference(spm,[status(thm)],[208,149,theory(equality)]) ).
cnf(219,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(er,[status(thm)],[216,theory(equality)]) ).
cnf(220,plain,
( empty_set = relation_dom(X1)
| ~ empty(X1) ),
inference(spm,[status(thm)],[116,219,theory(equality)]) ).
cnf(224,negated_conjecture,
( relation_rng(empty_set) != empty_set
| ~ empty(empty_set) ),
inference(spm,[status(thm)],[80,220,theory(equality)]) ).
cnf(228,negated_conjecture,
( relation_rng(empty_set) != empty_set
| $false ),
inference(rw,[status(thm)],[224,82,theory(equality)]) ).
cnf(229,negated_conjecture,
relation_rng(empty_set) != empty_set,
inference(cn,[status(thm)],[228,theory(equality)]) ).
cnf(233,negated_conjecture,
~ empty(empty_set),
inference(spm,[status(thm)],[229,204,theory(equality)]) ).
cnf(234,negated_conjecture,
$false,
inference(rw,[status(thm)],[233,82,theory(equality)]) ).
cnf(235,negated_conjecture,
$false,
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(236,negated_conjecture,
$false,
235,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU187+1.p
% --creating new selector for []
% -running prover on /tmp/tmpp2tEnq/sel_SEU187+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU187+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU187+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU187+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
%
%------------------------------------------------------------------------------