TSTP Solution File: SEU388+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU388+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 08:13:28 EST 2010
% Result : Theorem 0.71s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 61 ( 11 unt; 0 def)
% Number of atoms : 296 ( 32 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 368 ( 133 ~; 175 |; 43 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 0 sgn 45 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& topological_space(X2)
& top_str(X2)
& element(X3,the_carrier(X2)) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( point_neighbourhood(X4,X2,X3)
& X1 = X4 ) ) ),
file('/tmp/tmpaB99Ih/sel_SEU388+1.p_1',fraenkel_a_2_0_yellow19) ).
fof(13,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
file('/tmp/tmpaB99Ih/sel_SEU388+1.p_1',t3_yellow19) ).
fof(112,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
file('/tmp/tmpaB99Ih/sel_SEU388+1.p_1',d1_yellow19) ).
fof(120,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
inference(assume_negation,[status(cth)],[13]) ).
fof(121,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& topological_space(X2)
& top_str(X2)
& element(X3,the_carrier(X2)) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( point_neighbourhood(X4,X2,X3)
& X1 = X4 ) ) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(127,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[120,theory(equality)]) ).
fof(174,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[112,theory(equality)]) ).
fof(179,plain,
! [X1,X2,X3] :
( empty_carrier(X2)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2))
| ( ( ~ in(X1,a_2_0_yellow19(X2,X3))
| ? [X4] :
( point_neighbourhood(X4,X2,X3)
& X1 = X4 ) )
& ( ! [X4] :
( ~ point_neighbourhood(X4,X2,X3)
| X1 != X4 )
| in(X1,a_2_0_yellow19(X2,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[121]) ).
fof(180,plain,
! [X5,X6,X7] :
( empty_carrier(X6)
| ~ topological_space(X6)
| ~ top_str(X6)
| ~ element(X7,the_carrier(X6))
| ( ( ~ in(X5,a_2_0_yellow19(X6,X7))
| ? [X8] :
( point_neighbourhood(X8,X6,X7)
& X5 = X8 ) )
& ( ! [X9] :
( ~ point_neighbourhood(X9,X6,X7)
| X5 != X9 )
| in(X5,a_2_0_yellow19(X6,X7)) ) ) ),
inference(variable_rename,[status(thm)],[179]) ).
fof(181,plain,
! [X5,X6,X7] :
( empty_carrier(X6)
| ~ topological_space(X6)
| ~ top_str(X6)
| ~ element(X7,the_carrier(X6))
| ( ( ~ in(X5,a_2_0_yellow19(X6,X7))
| ( point_neighbourhood(esk1_3(X5,X6,X7),X6,X7)
& X5 = esk1_3(X5,X6,X7) ) )
& ( ! [X9] :
( ~ point_neighbourhood(X9,X6,X7)
| X5 != X9 )
| in(X5,a_2_0_yellow19(X6,X7)) ) ) ),
inference(skolemize,[status(esa)],[180]) ).
fof(182,plain,
! [X5,X6,X7,X9] :
( ( ( ~ point_neighbourhood(X9,X6,X7)
| X5 != X9
| in(X5,a_2_0_yellow19(X6,X7)) )
& ( ~ in(X5,a_2_0_yellow19(X6,X7))
| ( point_neighbourhood(esk1_3(X5,X6,X7),X6,X7)
& X5 = esk1_3(X5,X6,X7) ) ) )
| empty_carrier(X6)
| ~ topological_space(X6)
| ~ top_str(X6)
| ~ element(X7,the_carrier(X6)) ),
inference(shift_quantors,[status(thm)],[181]) ).
fof(183,plain,
! [X5,X6,X7,X9] :
( ( ~ point_neighbourhood(X9,X6,X7)
| X5 != X9
| in(X5,a_2_0_yellow19(X6,X7))
| empty_carrier(X6)
| ~ topological_space(X6)
| ~ top_str(X6)
| ~ element(X7,the_carrier(X6)) )
& ( point_neighbourhood(esk1_3(X5,X6,X7),X6,X7)
| ~ in(X5,a_2_0_yellow19(X6,X7))
| empty_carrier(X6)
| ~ topological_space(X6)
| ~ top_str(X6)
| ~ element(X7,the_carrier(X6)) )
& ( X5 = esk1_3(X5,X6,X7)
| ~ in(X5,a_2_0_yellow19(X6,X7))
| empty_carrier(X6)
| ~ topological_space(X6)
| ~ top_str(X6)
| ~ element(X7,the_carrier(X6)) ) ),
inference(distribute,[status(thm)],[182]) ).
cnf(184,plain,
( empty_carrier(X2)
| X3 = esk1_3(X3,X2,X1)
| ~ element(X1,the_carrier(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ in(X3,a_2_0_yellow19(X2,X1)) ),
inference(split_conjunct,[status(thm)],[183]) ).
cnf(185,plain,
( empty_carrier(X2)
| point_neighbourhood(esk1_3(X3,X2,X1),X2,X1)
| ~ element(X1,the_carrier(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| ~ in(X3,a_2_0_yellow19(X2,X1)) ),
inference(split_conjunct,[status(thm)],[183]) ).
cnf(186,plain,
( empty_carrier(X2)
| in(X3,a_2_0_yellow19(X2,X1))
| ~ element(X1,the_carrier(X2))
| ~ top_str(X2)
| ~ topological_space(X2)
| X3 != X4
| ~ point_neighbourhood(X4,X2,X1) ),
inference(split_conjunct,[status(thm)],[183]) ).
fof(244,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& ? [X2] :
( element(X2,the_carrier(X1))
& ? [X3] :
( ( ~ in(X3,neighborhood_system(X1,X2))
| ~ point_neighbourhood(X3,X1,X2) )
& ( in(X3,neighborhood_system(X1,X2))
| point_neighbourhood(X3,X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[127]) ).
fof(245,negated_conjecture,
? [X4] :
( ~ empty_carrier(X4)
& topological_space(X4)
& top_str(X4)
& ? [X5] :
( element(X5,the_carrier(X4))
& ? [X6] :
( ( ~ in(X6,neighborhood_system(X4,X5))
| ~ point_neighbourhood(X6,X4,X5) )
& ( in(X6,neighborhood_system(X4,X5))
| point_neighbourhood(X6,X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[244]) ).
fof(246,negated_conjecture,
( ~ empty_carrier(esk7_0)
& topological_space(esk7_0)
& top_str(esk7_0)
& element(esk8_0,the_carrier(esk7_0))
& ( ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0))
| ~ point_neighbourhood(esk9_0,esk7_0,esk8_0) )
& ( in(esk9_0,neighborhood_system(esk7_0,esk8_0))
| point_neighbourhood(esk9_0,esk7_0,esk8_0) ) ),
inference(skolemize,[status(esa)],[245]) ).
cnf(247,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| in(esk9_0,neighborhood_system(esk7_0,esk8_0)) ),
inference(split_conjunct,[status(thm)],[246]) ).
cnf(248,negated_conjecture,
( ~ point_neighbourhood(esk9_0,esk7_0,esk8_0)
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0)) ),
inference(split_conjunct,[status(thm)],[246]) ).
cnf(249,negated_conjecture,
element(esk8_0,the_carrier(esk7_0)),
inference(split_conjunct,[status(thm)],[246]) ).
cnf(250,negated_conjecture,
top_str(esk7_0),
inference(split_conjunct,[status(thm)],[246]) ).
cnf(251,negated_conjecture,
topological_space(esk7_0),
inference(split_conjunct,[status(thm)],[246]) ).
cnf(252,negated_conjecture,
~ empty_carrier(esk7_0),
inference(split_conjunct,[status(thm)],[246]) ).
fof(801,plain,
! [X1] :
( empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[174]) ).
fof(802,plain,
! [X3] :
( empty_carrier(X3)
| ~ topological_space(X3)
| ~ top_str(X3)
| ! [X4] :
( ~ element(X4,the_carrier(X3))
| neighborhood_system(X3,X4) = a_2_0_yellow19(X3,X4) ) ),
inference(variable_rename,[status(thm)],[801]) ).
fof(803,plain,
! [X3,X4] :
( ~ element(X4,the_carrier(X3))
| neighborhood_system(X3,X4) = a_2_0_yellow19(X3,X4)
| empty_carrier(X3)
| ~ topological_space(X3)
| ~ top_str(X3) ),
inference(shift_quantors,[status(thm)],[802]) ).
cnf(804,plain,
( empty_carrier(X1)
| neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[803]) ).
cnf(1161,negated_conjecture,
( a_2_0_yellow19(esk7_0,esk8_0) = neighborhood_system(esk7_0,esk8_0)
| empty_carrier(esk7_0)
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(spm,[status(thm)],[804,249,theory(equality)]) ).
cnf(1163,negated_conjecture,
( a_2_0_yellow19(esk7_0,esk8_0) = neighborhood_system(esk7_0,esk8_0)
| empty_carrier(esk7_0)
| $false
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[1161,250,theory(equality)]) ).
cnf(1164,negated_conjecture,
( a_2_0_yellow19(esk7_0,esk8_0) = neighborhood_system(esk7_0,esk8_0)
| empty_carrier(esk7_0)
| $false
| $false ),
inference(rw,[status(thm)],[1163,251,theory(equality)]) ).
cnf(1165,negated_conjecture,
( a_2_0_yellow19(esk7_0,esk8_0) = neighborhood_system(esk7_0,esk8_0)
| empty_carrier(esk7_0) ),
inference(cn,[status(thm)],[1164,theory(equality)]) ).
cnf(1166,negated_conjecture,
a_2_0_yellow19(esk7_0,esk8_0) = neighborhood_system(esk7_0,esk8_0),
inference(sr,[status(thm)],[1165,252,theory(equality)]) ).
cnf(1325,plain,
( in(X1,a_2_0_yellow19(X2,X3))
| empty_carrier(X2)
| ~ point_neighbourhood(X1,X2,X3)
| ~ element(X3,the_carrier(X2))
| ~ top_str(X2)
| ~ topological_space(X2) ),
inference(er,[status(thm)],[186,theory(equality)]) ).
cnf(1636,negated_conjecture,
( esk1_3(X1,esk7_0,esk8_0) = X1
| empty_carrier(esk7_0)
| ~ in(X1,neighborhood_system(esk7_0,esk8_0))
| ~ element(esk8_0,the_carrier(esk7_0))
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(spm,[status(thm)],[184,1166,theory(equality)]) ).
cnf(1637,negated_conjecture,
( esk1_3(X1,esk7_0,esk8_0) = X1
| empty_carrier(esk7_0)
| ~ in(X1,neighborhood_system(esk7_0,esk8_0))
| $false
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[1636,249,theory(equality)]) ).
cnf(1638,negated_conjecture,
( esk1_3(X1,esk7_0,esk8_0) = X1
| empty_carrier(esk7_0)
| ~ in(X1,neighborhood_system(esk7_0,esk8_0))
| $false
| $false
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[1637,250,theory(equality)]) ).
cnf(1639,negated_conjecture,
( esk1_3(X1,esk7_0,esk8_0) = X1
| empty_carrier(esk7_0)
| ~ in(X1,neighborhood_system(esk7_0,esk8_0))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1638,251,theory(equality)]) ).
cnf(1640,negated_conjecture,
( esk1_3(X1,esk7_0,esk8_0) = X1
| empty_carrier(esk7_0)
| ~ in(X1,neighborhood_system(esk7_0,esk8_0)) ),
inference(cn,[status(thm)],[1639,theory(equality)]) ).
cnf(1641,negated_conjecture,
( esk1_3(X1,esk7_0,esk8_0) = X1
| ~ in(X1,neighborhood_system(esk7_0,esk8_0)) ),
inference(sr,[status(thm)],[1640,252,theory(equality)]) ).
cnf(1754,negated_conjecture,
( esk1_3(esk9_0,esk7_0,esk8_0) = esk9_0
| point_neighbourhood(esk9_0,esk7_0,esk8_0) ),
inference(spm,[status(thm)],[1641,247,theory(equality)]) ).
cnf(1758,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| empty_carrier(esk7_0)
| ~ in(esk9_0,a_2_0_yellow19(esk7_0,esk8_0))
| ~ element(esk8_0,the_carrier(esk7_0))
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(spm,[status(thm)],[185,1754,theory(equality)]) ).
cnf(1759,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| empty_carrier(esk7_0)
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0))
| ~ element(esk8_0,the_carrier(esk7_0))
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[1758,1166,theory(equality)]) ).
cnf(1760,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| empty_carrier(esk7_0)
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0))
| $false
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[1759,249,theory(equality)]) ).
cnf(1761,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| empty_carrier(esk7_0)
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0))
| $false
| $false
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[1760,250,theory(equality)]) ).
cnf(1762,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| empty_carrier(esk7_0)
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0))
| $false
| $false
| $false ),
inference(rw,[status(thm)],[1761,251,theory(equality)]) ).
cnf(1763,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| empty_carrier(esk7_0)
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0)) ),
inference(cn,[status(thm)],[1762,theory(equality)]) ).
cnf(1764,negated_conjecture,
( point_neighbourhood(esk9_0,esk7_0,esk8_0)
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0)) ),
inference(sr,[status(thm)],[1763,252,theory(equality)]) ).
cnf(1765,negated_conjecture,
point_neighbourhood(esk9_0,esk7_0,esk8_0),
inference(csr,[status(thm)],[1764,247]) ).
cnf(1773,negated_conjecture,
( $false
| ~ in(esk9_0,neighborhood_system(esk7_0,esk8_0)) ),
inference(rw,[status(thm)],[248,1765,theory(equality)]) ).
cnf(1774,negated_conjecture,
~ in(esk9_0,neighborhood_system(esk7_0,esk8_0)),
inference(cn,[status(thm)],[1773,theory(equality)]) ).
cnf(6754,negated_conjecture,
( in(X1,neighborhood_system(esk7_0,esk8_0))
| empty_carrier(esk7_0)
| ~ point_neighbourhood(X1,esk7_0,esk8_0)
| ~ element(esk8_0,the_carrier(esk7_0))
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(spm,[status(thm)],[1325,1166,theory(equality)]) ).
cnf(6764,negated_conjecture,
( in(X1,neighborhood_system(esk7_0,esk8_0))
| empty_carrier(esk7_0)
| ~ point_neighbourhood(X1,esk7_0,esk8_0)
| $false
| ~ top_str(esk7_0)
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[6754,249,theory(equality)]) ).
cnf(6765,negated_conjecture,
( in(X1,neighborhood_system(esk7_0,esk8_0))
| empty_carrier(esk7_0)
| ~ point_neighbourhood(X1,esk7_0,esk8_0)
| $false
| $false
| ~ topological_space(esk7_0) ),
inference(rw,[status(thm)],[6764,250,theory(equality)]) ).
cnf(6766,negated_conjecture,
( in(X1,neighborhood_system(esk7_0,esk8_0))
| empty_carrier(esk7_0)
| ~ point_neighbourhood(X1,esk7_0,esk8_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[6765,251,theory(equality)]) ).
cnf(6767,negated_conjecture,
( in(X1,neighborhood_system(esk7_0,esk8_0))
| empty_carrier(esk7_0)
| ~ point_neighbourhood(X1,esk7_0,esk8_0) ),
inference(cn,[status(thm)],[6766,theory(equality)]) ).
cnf(6768,negated_conjecture,
( in(X1,neighborhood_system(esk7_0,esk8_0))
| ~ point_neighbourhood(X1,esk7_0,esk8_0) ),
inference(sr,[status(thm)],[6767,252,theory(equality)]) ).
cnf(6775,negated_conjecture,
~ point_neighbourhood(esk9_0,esk7_0,esk8_0),
inference(spm,[status(thm)],[1774,6768,theory(equality)]) ).
cnf(6788,negated_conjecture,
$false,
inference(rw,[status(thm)],[6775,1765,theory(equality)]) ).
cnf(6789,negated_conjecture,
$false,
inference(cn,[status(thm)],[6788,theory(equality)]) ).
cnf(6790,negated_conjecture,
$false,
6789,
[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/SEU388+1.p
% --creating new selector for []
% -running prover on /tmp/tmpaB99Ih/sel_SEU388+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU388+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU388+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU388+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
%
%------------------------------------------------------------------------------