TSTP Solution File: SEU170+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU170+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 05:04:29 EST 2010
% Result : Theorem 81.70s
% Output : CNFRefutation 81.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 92 ( 32 unt; 0 def)
% Number of atoms : 264 ( 57 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 274 ( 102 ~; 108 |; 42 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 157 ( 5 sgn 99 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t39_xboole_1) ).
fof(20,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(set_difference(X1,X3),set_difference(X2,X3)) ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t33_xboole_1) ).
fof(35,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',d1_zfmisc_1) ).
fof(37,axiom,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t7_xboole_1) ).
fof(39,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t48_xboole_1) ).
fof(58,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',commutativity_k2_xboole_0) ).
fof(61,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',fc1_subset_1) ).
fof(65,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',d2_subset_1) ).
fof(67,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',d7_xboole_0) ).
fof(72,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',d5_subset_1) ).
fof(85,axiom,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t40_xboole_1) ).
fof(88,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t63_xboole_1) ).
fof(90,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t37_xboole_1) ).
fof(99,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t43_subset_1) ).
fof(110,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/tmp/tmpVYGE3k/sel_SEU170+2.p_2',t83_xboole_1) ).
fof(111,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
inference(assume_negation,[status(cth)],[99]) ).
fof(122,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[61,theory(equality)]) ).
fof(123,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[65,theory(equality)]) ).
fof(134,plain,
! [X3,X4] : set_union2(X3,set_difference(X4,X3)) = set_union2(X3,X4),
inference(variable_rename,[status(thm)],[2]) ).
cnf(135,plain,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[134]) ).
fof(191,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| subset(set_difference(X1,X3),set_difference(X2,X3)) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(192,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| subset(set_difference(X4,X6),set_difference(X5,X6)) ),
inference(variable_rename,[status(thm)],[191]) ).
cnf(193,plain,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[192]) ).
fof(244,plain,
! [X1,X2] :
( ( X2 != powerset(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| subset(X3,X1) )
& ( ~ subset(X3,X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ subset(X3,X1) )
& ( in(X3,X2)
| subset(X3,X1) ) )
| X2 = powerset(X1) ) ),
inference(fof_nnf,[status(thm)],[35]) ).
fof(245,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ subset(X7,X4) )
& ( in(X7,X5)
| subset(X7,X4) ) )
| X5 = powerset(X4) ) ),
inference(variable_rename,[status(thm)],[244]) ).
fof(246,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| ~ subset(esk6_2(X4,X5),X4) )
& ( in(esk6_2(X4,X5),X5)
| subset(esk6_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(skolemize,[status(esa)],[245]) ).
fof(247,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) )
| X5 != powerset(X4) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| ~ subset(esk6_2(X4,X5),X4) )
& ( in(esk6_2(X4,X5),X5)
| subset(esk6_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(shift_quantors,[status(thm)],[246]) ).
fof(248,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk6_2(X4,X5),X5)
| ~ subset(esk6_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk6_2(X4,X5),X5)
| subset(esk6_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
inference(distribute,[status(thm)],[247]) ).
cnf(252,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[248]) ).
fof(255,plain,
! [X3,X4] : subset(X3,set_union2(X3,X4)),
inference(variable_rename,[status(thm)],[37]) ).
cnf(256,plain,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[255]) ).
fof(258,plain,
! [X3,X4] : set_difference(X3,set_difference(X3,X4)) = set_intersection2(X3,X4),
inference(variable_rename,[status(thm)],[39]) ).
cnf(259,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[258]) ).
fof(325,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[58]) ).
cnf(326,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[325]) ).
fof(336,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[122]) ).
cnf(337,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[336]) ).
fof(348,plain,
! [X1,X2] :
( ( empty(X1)
| ( ( ~ element(X2,X1)
| in(X2,X1) )
& ( ~ in(X2,X1)
| element(X2,X1) ) ) )
& ( ~ empty(X1)
| ( ( ~ element(X2,X1)
| empty(X2) )
& ( ~ empty(X2)
| element(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[123]) ).
fof(349,plain,
! [X3,X4] :
( ( empty(X3)
| ( ( ~ element(X4,X3)
| in(X4,X3) )
& ( ~ in(X4,X3)
| element(X4,X3) ) ) )
& ( ~ empty(X3)
| ( ( ~ element(X4,X3)
| empty(X4) )
& ( ~ empty(X4)
| element(X4,X3) ) ) ) ),
inference(variable_rename,[status(thm)],[348]) ).
fof(350,plain,
! [X3,X4] :
( ( ~ element(X4,X3)
| in(X4,X3)
| empty(X3) )
& ( ~ in(X4,X3)
| element(X4,X3)
| empty(X3) )
& ( ~ element(X4,X3)
| empty(X4)
| ~ empty(X3) )
& ( ~ empty(X4)
| element(X4,X3)
| ~ empty(X3) ) ),
inference(distribute,[status(thm)],[349]) ).
cnf(354,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[350]) ).
fof(356,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set )
& ( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[67]) ).
fof(357,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_intersection2(X3,X4) = empty_set )
& ( set_intersection2(X3,X4) != empty_set
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[356]) ).
cnf(358,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[357]) ).
fof(373,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(fof_nnf,[status(thm)],[72]) ).
fof(374,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[373]) ).
cnf(375,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[374]) ).
fof(428,plain,
! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
inference(variable_rename,[status(thm)],[85]) ).
cnf(429,plain,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[428]) ).
fof(437,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ disjoint(X2,X3)
| disjoint(X1,X3) ),
inference(fof_nnf,[status(thm)],[88]) ).
fof(438,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ disjoint(X5,X6)
| disjoint(X4,X6) ),
inference(variable_rename,[status(thm)],[437]) ).
cnf(439,plain,
( disjoint(X1,X2)
| ~ disjoint(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[438]) ).
fof(443,plain,
! [X1,X2] :
( ( set_difference(X1,X2) != empty_set
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[90]) ).
fof(444,plain,
! [X3,X4] :
( ( set_difference(X3,X4) != empty_set
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| set_difference(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[443]) ).
cnf(445,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[444]) ).
fof(493,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(X1))
& ? [X3] :
( element(X3,powerset(X1))
& ( ~ disjoint(X2,X3)
| ~ subset(X2,subset_complement(X1,X3)) )
& ( disjoint(X2,X3)
| subset(X2,subset_complement(X1,X3)) ) ) ),
inference(fof_nnf,[status(thm)],[111]) ).
fof(494,negated_conjecture,
? [X4,X5] :
( element(X5,powerset(X4))
& ? [X6] :
( element(X6,powerset(X4))
& ( ~ disjoint(X5,X6)
| ~ subset(X5,subset_complement(X4,X6)) )
& ( disjoint(X5,X6)
| subset(X5,subset_complement(X4,X6)) ) ) ),
inference(variable_rename,[status(thm)],[493]) ).
fof(495,negated_conjecture,
( element(esk23_0,powerset(esk22_0))
& element(esk24_0,powerset(esk22_0))
& ( ~ disjoint(esk23_0,esk24_0)
| ~ subset(esk23_0,subset_complement(esk22_0,esk24_0)) )
& ( disjoint(esk23_0,esk24_0)
| subset(esk23_0,subset_complement(esk22_0,esk24_0)) ) ),
inference(skolemize,[status(esa)],[494]) ).
cnf(496,negated_conjecture,
( subset(esk23_0,subset_complement(esk22_0,esk24_0))
| disjoint(esk23_0,esk24_0) ),
inference(split_conjunct,[status(thm)],[495]) ).
cnf(497,negated_conjecture,
( ~ subset(esk23_0,subset_complement(esk22_0,esk24_0))
| ~ disjoint(esk23_0,esk24_0) ),
inference(split_conjunct,[status(thm)],[495]) ).
cnf(498,negated_conjecture,
element(esk24_0,powerset(esk22_0)),
inference(split_conjunct,[status(thm)],[495]) ).
cnf(499,negated_conjecture,
element(esk23_0,powerset(esk22_0)),
inference(split_conjunct,[status(thm)],[495]) ).
fof(544,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| set_difference(X1,X2) = X1 )
& ( set_difference(X1,X2) != X1
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[110]) ).
fof(545,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| set_difference(X3,X4) = X3 )
& ( set_difference(X3,X4) != X3
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[544]) ).
cnf(546,plain,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[545]) ).
cnf(547,plain,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[545]) ).
cnf(584,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[358,259,theory(equality)]),
[unfolding] ).
cnf(661,plain,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[256,326,theory(equality)]) ).
cnf(743,negated_conjecture,
subset_complement(esk22_0,esk24_0) = set_difference(esk22_0,esk24_0),
inference(spm,[status(thm)],[375,498,theory(equality)]) ).
cnf(751,negated_conjecture,
( empty(powerset(esk22_0))
| in(esk23_0,powerset(esk22_0)) ),
inference(spm,[status(thm)],[354,499,theory(equality)]) ).
cnf(758,negated_conjecture,
in(esk23_0,powerset(esk22_0)),
inference(sr,[status(thm)],[751,337,theory(equality)]) ).
cnf(896,plain,
( disjoint(X1,X2)
| ~ subset(X1,set_difference(X1,X2)) ),
inference(spm,[status(thm)],[584,445,theory(equality)]) ).
cnf(992,plain,
( subset(set_difference(X1,X2),set_difference(X3,X2))
| ~ subset(X1,set_union2(X3,X2)) ),
inference(spm,[status(thm)],[193,429,theory(equality)]) ).
cnf(2314,negated_conjecture,
( subset(esk23_0,X1)
| powerset(X1) != powerset(esk22_0) ),
inference(spm,[status(thm)],[252,758,theory(equality)]) ).
cnf(2402,negated_conjecture,
( ~ disjoint(esk23_0,esk24_0)
| ~ subset(esk23_0,set_difference(esk22_0,esk24_0)) ),
inference(rw,[status(thm)],[497,743,theory(equality)]) ).
cnf(2403,negated_conjecture,
( disjoint(esk23_0,esk24_0)
| subset(esk23_0,set_difference(esk22_0,esk24_0)) ),
inference(rw,[status(thm)],[496,743,theory(equality)]) ).
cnf(2417,plain,
( ~ subset(esk23_0,set_difference(esk22_0,esk24_0))
| set_difference(esk23_0,esk24_0) != esk23_0 ),
inference(spm,[status(thm)],[2402,546,theory(equality)]) ).
cnf(2419,negated_conjecture,
( set_difference(esk23_0,esk24_0) = esk23_0
| subset(esk23_0,set_difference(esk22_0,esk24_0)) ),
inference(spm,[status(thm)],[547,2403,theory(equality)]) ).
cnf(2546,negated_conjecture,
subset(esk23_0,esk22_0),
inference(er,[status(thm)],[2314,theory(equality)]) ).
cnf(5804,negated_conjecture,
( disjoint(esk23_0,X1)
| set_difference(esk23_0,esk24_0) = esk23_0
| ~ disjoint(set_difference(esk22_0,esk24_0),X1) ),
inference(spm,[status(thm)],[439,2419,theory(equality)]) ).
cnf(12232,plain,
( disjoint(set_difference(X1,X2),X2)
| ~ subset(X1,set_union2(set_difference(X1,X2),X2)) ),
inference(spm,[status(thm)],[896,992,theory(equality)]) ).
cnf(12263,plain,
( disjoint(set_difference(X1,X2),X2)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[12232,326,theory(equality)]),135,theory(equality)]),661,theory(equality)]) ).
cnf(12264,plain,
disjoint(set_difference(X1,X2),X2),
inference(cn,[status(thm)],[12263,theory(equality)]) ).
cnf(585450,plain,
( set_difference(esk23_0,esk24_0) = esk23_0
| disjoint(esk23_0,esk24_0) ),
inference(spm,[status(thm)],[5804,12264,theory(equality)]) ).
cnf(586245,plain,
set_difference(esk23_0,esk24_0) = esk23_0,
inference(csr,[status(thm)],[585450,547]) ).
cnf(586297,plain,
( subset(esk23_0,set_difference(X1,esk24_0))
| ~ subset(esk23_0,X1) ),
inference(spm,[status(thm)],[193,586245,theory(equality)]) ).
cnf(586731,plain,
( $false
| ~ subset(esk23_0,set_difference(esk22_0,esk24_0)) ),
inference(rw,[status(thm)],[2417,586245,theory(equality)]) ).
cnf(586732,plain,
~ subset(esk23_0,set_difference(esk22_0,esk24_0)),
inference(cn,[status(thm)],[586731,theory(equality)]) ).
cnf(678882,plain,
~ subset(esk23_0,esk22_0),
inference(spm,[status(thm)],[586732,586297,theory(equality)]) ).
cnf(679094,plain,
$false,
inference(rw,[status(thm)],[678882,2546,theory(equality)]) ).
cnf(679095,plain,
$false,
inference(cn,[status(thm)],[679094,theory(equality)]) ).
cnf(679096,plain,
$false,
679095,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU170+2.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpVYGE3k/sel_SEU170+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpVYGE3k/sel_SEU170+2.p_2 with time limit 79
% -prover status Theorem
% Problem SEU170+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU170+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU170+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
%
%------------------------------------------------------------------------------