%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU174+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 05:05:49 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 83 ( 28 unt; 0 def)
% Number of atoms : 243 ( 43 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 284 ( 124 ~; 112 |; 34 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 130 ( 15 sgn 78 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',t1_subset) ).
fof(6,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',involutiveness_k7_setfam_1) ).
fof(8,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',t4_subset) ).
fof(10,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',fc1_subset_1) ).
fof(12,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',t46_setfam_1) ).
fof(13,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',t5_subset) ).
fof(15,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',t2_subset) ).
fof(18,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',existence_m1_subset_1) ).
fof(19,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',d8_setfam_1) ).
fof(20,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',t6_boole) ).
fof(21,axiom,
empty(empty_set),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',fc1_xboole_0) ).
fof(24,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/tmp/tmp_4dASe/sel_SEU174+1.p_1',rc2_subset_1) ).
fof(28,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(31,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(48,plain,
! [X1,X2] :
( ~ in(X1,X2)
| element(X1,X2) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(49,plain,
! [X3,X4] :
( ~ in(X3,X4)
| element(X3,X4) ),
inference(variable_rename,[status(thm)],[48]) ).
cnf(50,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(51,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(52,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| complements_of_subsets(X3,complements_of_subsets(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[51]) ).
cnf(53,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(56,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(57,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[56]) ).
cnf(58,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[57]) ).
fof(62,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[31]) ).
cnf(63,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[62]) ).
fof(67,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(powerset(X1)))
& X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(68,negated_conjecture,
? [X3,X4] :
( element(X4,powerset(powerset(X3)))
& X4 != empty_set
& complements_of_subsets(X3,X4) = empty_set ),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,negated_conjecture,
( element(esk4_0,powerset(powerset(esk3_0)))
& esk4_0 != empty_set
& complements_of_subsets(esk3_0,esk4_0) = empty_set ),
inference(skolemize,[status(esa)],[68]) ).
cnf(70,negated_conjecture,
complements_of_subsets(esk3_0,esk4_0) = empty_set,
inference(split_conjunct,[status(thm)],[69]) ).
cnf(71,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[69]) ).
cnf(72,negated_conjecture,
element(esk4_0,powerset(powerset(esk3_0))),
inference(split_conjunct,[status(thm)],[69]) ).
fof(73,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(74,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| ~ empty(X6) ),
inference(variable_rename,[status(thm)],[73]) ).
cnf(75,plain,
( ~ empty(X1)
| ~ element(X2,powerset(X1))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[74]) ).
fof(79,plain,
! [X1,X2] :
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(80,plain,
! [X3,X4] :
( ~ element(X3,X4)
| empty(X4)
| in(X3,X4) ),
inference(variable_rename,[status(thm)],[79]) ).
cnf(81,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[80]) ).
fof(87,plain,
! [X3] :
? [X4] : element(X4,X3),
inference(variable_rename,[status(thm)],[18]) ).
fof(88,plain,
! [X3] : element(esk5_1(X3),X3),
inference(skolemize,[status(esa)],[87]) ).
cnf(89,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[88]) ).
fof(90,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| ! [X3] :
( ~ element(X3,powerset(powerset(X1)))
| ( ( X3 != complements_of_subsets(X1,X2)
| ! [X4] :
( ~ element(X4,powerset(X1))
| ( ( ~ in(X4,X3)
| in(subset_complement(X1,X4),X2) )
& ( ~ in(subset_complement(X1,X4),X2)
| in(X4,X3) ) ) ) )
& ( ? [X4] :
( element(X4,powerset(X1))
& ( ~ in(X4,X3)
| ~ in(subset_complement(X1,X4),X2) )
& ( in(X4,X3)
| in(subset_complement(X1,X4),X2) ) )
| X3 = complements_of_subsets(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(91,plain,
! [X5,X6] :
( ~ element(X6,powerset(powerset(X5)))
| ! [X7] :
( ~ element(X7,powerset(powerset(X5)))
| ( ( X7 != complements_of_subsets(X5,X6)
| ! [X8] :
( ~ element(X8,powerset(X5))
| ( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7) ) ) ) )
& ( ? [X9] :
( element(X9,powerset(X5))
& ( ~ in(X9,X7)
| ~ in(subset_complement(X5,X9),X6) )
& ( in(X9,X7)
| in(subset_complement(X5,X9),X6) ) )
| X7 = complements_of_subsets(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[90]) ).
fof(92,plain,
! [X5,X6] :
( ~ element(X6,powerset(powerset(X5)))
| ! [X7] :
( ~ element(X7,powerset(powerset(X5)))
| ( ( X7 != complements_of_subsets(X5,X6)
| ! [X8] :
( ~ element(X8,powerset(X5))
| ( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7) ) ) ) )
& ( ( element(esk6_3(X5,X6,X7),powerset(X5))
& ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk6_3(X5,X6,X7)),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk6_3(X5,X6,X7)),X6) ) )
| X7 = complements_of_subsets(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[91]) ).
fof(93,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,powerset(X5))
| ( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7) ) )
| X7 != complements_of_subsets(X5,X6) )
& ( ( element(esk6_3(X5,X6,X7),powerset(X5))
& ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk6_3(X5,X6,X7)),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk6_3(X5,X6,X7)),X6) ) )
| X7 = complements_of_subsets(X5,X6) ) )
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) ),
inference(shift_quantors,[status(thm)],[92]) ).
fof(94,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( element(esk6_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk6_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk6_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk6_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk6_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) ) ),
inference(distribute,[status(thm)],[93]) ).
cnf(99,plain,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[94]) ).
fof(100,plain,
! [X1] :
( ~ empty(X1)
| X1 = empty_set ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(101,plain,
! [X2] :
( ~ empty(X2)
| X2 = empty_set ),
inference(variable_rename,[status(thm)],[100]) ).
cnf(102,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[101]) ).
cnf(103,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[21]) ).
fof(106,plain,
! [X3] :
? [X4] :
( element(X4,powerset(X3))
& empty(X4) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(107,plain,
! [X3] :
( element(esk7_1(X3),powerset(X3))
& empty(esk7_1(X3)) ),
inference(skolemize,[status(esa)],[106]) ).
cnf(108,plain,
empty(esk7_1(X1)),
inference(split_conjunct,[status(thm)],[107]) ).
cnf(109,plain,
element(esk7_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[107]) ).
cnf(125,plain,
empty_set = esk7_1(X1),
inference(spm,[status(thm)],[102,108,theory(equality)]) ).
cnf(132,plain,
( in(esk5_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[81,89,theory(equality)]) ).
cnf(133,plain,
( in(esk7_1(X1),powerset(X1))
| empty(powerset(X1)) ),
inference(spm,[status(thm)],[81,109,theory(equality)]) ).
cnf(136,plain,
in(esk7_1(X1),powerset(X1)),
inference(sr,[status(thm)],[133,63,theory(equality)]) ).
cnf(145,negated_conjecture,
( complements_of_subsets(esk3_0,empty_set) = esk4_0
| ~ element(esk4_0,powerset(powerset(esk3_0))) ),
inference(spm,[status(thm)],[53,70,theory(equality)]) ).
cnf(147,negated_conjecture,
( complements_of_subsets(esk3_0,empty_set) = esk4_0
| $false ),
inference(rw,[status(thm)],[145,72,theory(equality)]) ).
cnf(148,negated_conjecture,
complements_of_subsets(esk3_0,empty_set) = esk4_0,
inference(cn,[status(thm)],[147,theory(equality)]) ).
cnf(173,plain,
( in(subset_complement(X2,X4),X1)
| complements_of_subsets(X2,X1) != X3
| ~ in(X4,X3)
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(csr,[status(thm)],[99,58]) ).
cnf(174,negated_conjecture,
( in(subset_complement(esk3_0,X1),X2)
| complements_of_subsets(esk3_0,X2) != esk4_0
| ~ in(X1,esk4_0)
| ~ element(X2,powerset(powerset(esk3_0))) ),
inference(spm,[status(thm)],[173,72,theory(equality)]) ).
cnf(226,plain,
in(empty_set,powerset(X1)),
inference(rw,[status(thm)],[136,125,theory(equality)]) ).
cnf(230,plain,
element(empty_set,powerset(X1)),
inference(spm,[status(thm)],[50,226,theory(equality)]) ).
cnf(235,plain,
( ~ in(X1,empty_set)
| ~ empty(X2) ),
inference(spm,[status(thm)],[75,230,theory(equality)]) ).
fof(279,plain,
( ~ epred1_0
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(definition),
[split] ).
cnf(280,plain,
( epred1_0
| ~ in(X1,empty_set) ),
inference(split_equiv,[status(thm)],[279]) ).
fof(281,plain,
( ~ epred2_0
<=> ! [X2] : ~ empty(X2) ),
introduced(definition),
[split] ).
cnf(282,plain,
( epred2_0
| ~ empty(X2) ),
inference(split_equiv,[status(thm)],[281]) ).
cnf(283,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[235,279,theory(equality)]),281,theory(equality)]),
[split] ).
cnf(291,plain,
epred2_0,
inference(spm,[status(thm)],[282,103,theory(equality)]) ).
cnf(293,plain,
( $false
| ~ epred1_0 ),
inference(rw,[status(thm)],[283,291,theory(equality)]) ).
cnf(294,plain,
~ epred1_0,
inference(cn,[status(thm)],[293,theory(equality)]) ).
cnf(295,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[280,294,theory(equality)]) ).
cnf(669,negated_conjecture,
( complements_of_subsets(esk3_0,empty_set) != esk4_0
| ~ in(X1,esk4_0)
| ~ element(empty_set,powerset(powerset(esk3_0))) ),
inference(spm,[status(thm)],[295,174,theory(equality)]) ).
cnf(695,negated_conjecture,
( $false
| ~ in(X1,esk4_0)
| ~ element(empty_set,powerset(powerset(esk3_0))) ),
inference(rw,[status(thm)],[669,148,theory(equality)]) ).
cnf(696,negated_conjecture,
( $false
| ~ in(X1,esk4_0)
| $false ),
inference(rw,[status(thm)],[695,230,theory(equality)]) ).
cnf(697,negated_conjecture,
~ in(X1,esk4_0),
inference(cn,[status(thm)],[696,theory(equality)]) ).
cnf(705,negated_conjecture,
empty(esk4_0),
inference(spm,[status(thm)],[697,132,theory(equality)]) ).
cnf(710,negated_conjecture,
empty_set = esk4_0,
inference(spm,[status(thm)],[102,705,theory(equality)]) ).
cnf(728,negated_conjecture,
$false,
inference(sr,[status(thm)],[710,71,theory(equality)]) ).
cnf(729,negated_conjecture,
$false,
728,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU174+1.p
% --creating new selector for []
% -running prover on /tmp/tmp_4dASe/sel_SEU174+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU174+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU174+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU174+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
%
%------------------------------------------------------------------------------