TSTP Solution File: SET679+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET679+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:10:35 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 10 unt; 0 def)
% Number of atoms : 186 ( 14 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 229 ( 95 ~; 90 |; 27 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 3 sgn 43 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> not_equal(identity_relation_of(X1),empty_set) ),
file('/tmp/tmpMCWG3U/sel_SET679+3.p_1',prove_relset_1_46) ).
fof(6,axiom,
! [X1] : ilf_type(X1,set_type),
file('/tmp/tmpMCWG3U/sel_SET679+3.p_1',p22) ).
fof(17,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
file('/tmp/tmpMCWG3U/sel_SET679+3.p_1',p2) ).
fof(18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
<=> member(ordered_pair(X2,X2),identity_relation_of(X1)) ) ) ),
file('/tmp/tmpMCWG3U/sel_SET679+3.p_1',p1) ).
fof(20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( not_equal(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpMCWG3U/sel_SET679+3.p_1',p7) ).
fof(23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/tmp/tmpMCWG3U/sel_SET679+3.p_1',p8) ).
fof(25,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> not_equal(identity_relation_of(X1),empty_set) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(26,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> not_equal(identity_relation_of(X1),empty_set) ),
inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).
fof(30,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,empty_set) ),
inference(fof_simplification,[status(thm)],[17,theory(equality)]) ).
fof(31,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[23,theory(equality)]) ).
fof(34,negated_conjecture,
? [X1] :
( ~ empty(X1)
& ilf_type(X1,set_type)
& ~ not_equal(identity_relation_of(X1),empty_set) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(35,negated_conjecture,
? [X2] :
( ~ empty(X2)
& ilf_type(X2,set_type)
& ~ not_equal(identity_relation_of(X2),empty_set) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( ~ empty(esk1_0)
& ilf_type(esk1_0,set_type)
& ~ not_equal(identity_relation_of(esk1_0),empty_set) ),
inference(skolemize,[status(esa)],[35]) ).
cnf(37,negated_conjecture,
~ not_equal(identity_relation_of(esk1_0),empty_set),
inference(split_conjunct,[status(thm)],[36]) ).
cnf(39,negated_conjecture,
~ empty(esk1_0),
inference(split_conjunct,[status(thm)],[36]) ).
fof(50,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[6]) ).
cnf(51,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[50]) ).
fof(107,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,empty_set) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(108,plain,
! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,empty_set) ),
inference(variable_rename,[status(thm)],[107]) ).
cnf(109,plain,
( ~ member(X1,empty_set)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[108]) ).
fof(110,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ member(X2,X1)
| member(ordered_pair(X2,X2),identity_relation_of(X1)) )
& ( ~ member(ordered_pair(X2,X2),identity_relation_of(X1))
| member(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(111,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ member(X4,X3)
| member(ordered_pair(X4,X4),identity_relation_of(X3)) )
& ( ~ member(ordered_pair(X4,X4),identity_relation_of(X3))
| member(X4,X3) ) ) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ member(X4,X3)
| member(ordered_pair(X4,X4),identity_relation_of(X3)) )
& ( ~ member(ordered_pair(X4,X4),identity_relation_of(X3))
| member(X4,X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[111]) ).
fof(113,plain,
! [X3,X4] :
( ( ~ member(X4,X3)
| member(ordered_pair(X4,X4),identity_relation_of(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ member(ordered_pair(X4,X4),identity_relation_of(X3))
| member(X4,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[112]) ).
cnf(115,plain,
( member(ordered_pair(X2,X2),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[113]) ).
fof(126,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ( ( ~ not_equal(X1,X2)
| X1 != X2 )
& ( X1 = X2
| not_equal(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(127,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ not_equal(X3,X4)
| X3 != X4 )
& ( X3 = X4
| not_equal(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[126]) ).
fof(128,plain,
! [X3,X4] :
( ~ ilf_type(X4,set_type)
| ( ( ~ not_equal(X3,X4)
| X3 != X4 )
& ( X3 = X4
| not_equal(X3,X4) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[127]) ).
fof(129,plain,
! [X3,X4] :
( ( ~ not_equal(X3,X4)
| X3 != X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( X3 = X4
| not_equal(X3,X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[128]) ).
cnf(130,plain,
( not_equal(X1,X2)
| X1 = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[129]) ).
fof(142,plain,
! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ empty(X1)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X1) )
| empty(X1) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(143,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ? [X5] :
( ilf_type(X5,set_type)
& member(X5,X3) )
| empty(X3) ) ) ),
inference(variable_rename,[status(thm)],[142]) ).
fof(144,plain,
! [X3] :
( ~ ilf_type(X3,set_type)
| ( ( ~ empty(X3)
| ! [X4] :
( ~ ilf_type(X4,set_type)
| ~ member(X4,X3) ) )
& ( ( ilf_type(esk10_1(X3),set_type)
& member(esk10_1(X3),X3) )
| empty(X3) ) ) ),
inference(skolemize,[status(esa)],[143]) ).
fof(145,plain,
! [X3,X4] :
( ( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3) )
& ( ( ilf_type(esk10_1(X3),set_type)
& member(esk10_1(X3),X3) )
| empty(X3) ) )
| ~ ilf_type(X3,set_type) ),
inference(shift_quantors,[status(thm)],[144]) ).
fof(146,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ empty(X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk10_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk10_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[145]) ).
cnf(147,plain,
( empty(X1)
| member(esk10_1(X1),X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[146]) ).
cnf(161,plain,
( $false
| ~ member(X1,empty_set) ),
inference(rw,[status(thm)],[109,51,theory(equality)]) ).
cnf(162,plain,
~ member(X1,empty_set),
inference(cn,[status(thm)],[161,theory(equality)]) ).
cnf(176,plain,
( X1 = X2
| not_equal(X1,X2)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[130,51,theory(equality)]) ).
cnf(177,plain,
( X1 = X2
| not_equal(X1,X2)
| $false
| $false ),
inference(rw,[status(thm)],[176,51,theory(equality)]) ).
cnf(178,plain,
( X1 = X2
| not_equal(X1,X2) ),
inference(cn,[status(thm)],[177,theory(equality)]) ).
cnf(179,negated_conjecture,
identity_relation_of(esk1_0) = empty_set,
inference(spm,[status(thm)],[37,178,theory(equality)]) ).
cnf(189,plain,
( empty(X1)
| member(esk10_1(X1),X1)
| $false ),
inference(rw,[status(thm)],[147,51,theory(equality)]) ).
cnf(190,plain,
( empty(X1)
| member(esk10_1(X1),X1) ),
inference(cn,[status(thm)],[189,theory(equality)]) ).
cnf(246,plain,
( member(ordered_pair(X2,X2),identity_relation_of(X1))
| ~ member(X2,X1)
| $false
| ~ ilf_type(X1,set_type) ),
inference(rw,[status(thm)],[115,51,theory(equality)]) ).
cnf(247,plain,
( member(ordered_pair(X2,X2),identity_relation_of(X1))
| ~ member(X2,X1)
| $false
| $false ),
inference(rw,[status(thm)],[246,51,theory(equality)]) ).
cnf(248,plain,
( member(ordered_pair(X2,X2),identity_relation_of(X1))
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[247,theory(equality)]) ).
cnf(249,plain,
( member(ordered_pair(esk10_1(X1),esk10_1(X1)),identity_relation_of(X1))
| empty(X1) ),
inference(spm,[status(thm)],[248,190,theory(equality)]) ).
cnf(403,negated_conjecture,
( member(ordered_pair(esk10_1(esk1_0),esk10_1(esk1_0)),empty_set)
| empty(esk1_0) ),
inference(spm,[status(thm)],[249,179,theory(equality)]) ).
cnf(409,negated_conjecture,
empty(esk1_0),
inference(sr,[status(thm)],[403,162,theory(equality)]) ).
cnf(410,negated_conjecture,
$false,
inference(sr,[status(thm)],[409,39,theory(equality)]) ).
cnf(411,negated_conjecture,
$false,
410,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET679+3.p
% --creating new selector for []
% -running prover on /tmp/tmpMCWG3U/sel_SET679+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET679+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET679+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET679+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
%
%------------------------------------------------------------------------------