TSTP Solution File: SET812+4 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET812+4 : TPTP v5.0.0. Released v3.2.0.
% 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 03:41:21 EST 2010
% Result : Theorem 84.87s
% Output : CNFRefutation 84.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 7 unt; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 259 ( 99 ~; 100 |; 51 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 2 sgn 58 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',subset) ).
fof(2,axiom,
! [X1] :
( member(X1,on)
<=> ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( member(X3,X1)
=> subset(X3,X1) ) ) ),
file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',ordinal_number) ).
fof(5,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',equal_set) ).
fof(7,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',intersection) ).
fof(10,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',power_set) ).
fof(11,conjecture,
! [X1] :
( member(X1,on)
=> equal_set(X1,intersection(X1,power_set(X1))) ),
file('/tmp/tmpOf_kV2/sel_SET812+4.p_2',thV10) ).
fof(12,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> equal_set(X1,intersection(X1,power_set(X1))) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(13,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(14,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[14]) ).
fof(16,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[15]) ).
fof(17,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[16]) ).
cnf(18,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(19,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[17]) ).
cnf(20,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X1] :
( ( ~ member(X1,on)
| ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( ~ member(X3,X1)
| subset(X3,X1) ) ) )
& ( ~ set(X1)
| ~ strict_well_order(member_predicate,X1)
| ? [X3] :
( member(X3,X1)
& ~ subset(X3,X1) )
| member(X1,on) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(22,plain,
! [X4] :
( ( ~ member(X4,on)
| ( set(X4)
& strict_well_order(member_predicate,X4)
& ! [X5] :
( ~ member(X5,X4)
| subset(X5,X4) ) ) )
& ( ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| ? [X6] :
( member(X6,X4)
& ~ subset(X6,X4) )
| member(X4,on) ) ),
inference(variable_rename,[status(thm)],[21]) ).
fof(23,plain,
! [X4] :
( ( ~ member(X4,on)
| ( set(X4)
& strict_well_order(member_predicate,X4)
& ! [X5] :
( ~ member(X5,X4)
| subset(X5,X4) ) ) )
& ( ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| ( member(esk2_1(X4),X4)
& ~ subset(esk2_1(X4),X4) )
| member(X4,on) ) ),
inference(skolemize,[status(esa)],[22]) ).
fof(24,plain,
! [X4,X5] :
( ( ( ( ~ member(X5,X4)
| subset(X5,X4) )
& set(X4)
& strict_well_order(member_predicate,X4) )
| ~ member(X4,on) )
& ( ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| ( member(esk2_1(X4),X4)
& ~ subset(esk2_1(X4),X4) )
| member(X4,on) ) ),
inference(shift_quantors,[status(thm)],[23]) ).
fof(25,plain,
! [X4,X5] :
( ( ~ member(X5,X4)
| subset(X5,X4)
| ~ member(X4,on) )
& ( set(X4)
| ~ member(X4,on) )
& ( strict_well_order(member_predicate,X4)
| ~ member(X4,on) )
& ( member(esk2_1(X4),X4)
| ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| member(X4,on) )
& ( ~ subset(esk2_1(X4),X4)
| ~ set(X4)
| ~ strict_well_order(member_predicate,X4)
| member(X4,on) ) ),
inference(distribute,[status(thm)],[24]) ).
cnf(30,plain,
( subset(X2,X1)
| ~ member(X1,on)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[25]) ).
fof(45,plain,
! [X1,X2] :
( ( ~ equal_set(X1,X2)
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| equal_set(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(46,plain,
! [X3,X4] :
( ( ~ equal_set(X3,X4)
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,plain,
! [X3,X4] :
( ( subset(X3,X4)
| ~ equal_set(X3,X4) )
& ( subset(X4,X3)
| ~ equal_set(X3,X4) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| equal_set(X3,X4) ) ),
inference(distribute,[status(thm)],[46]) ).
cnf(48,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[47]) ).
fof(61,plain,
! [X3,X1,X2] :
( ( ~ member(X3,intersection(X1,X2))
| ( member(X3,X1)
& member(X3,X2) ) )
& ( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(62,plain,
! [X4,X5,X6] :
( ( ~ member(X4,intersection(X5,X6))
| ( member(X4,X5)
& member(X4,X6) ) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[61]) ).
fof(63,plain,
! [X4,X5,X6] :
( ( member(X4,X5)
| ~ member(X4,intersection(X5,X6)) )
& ( member(X4,X6)
| ~ member(X4,intersection(X5,X6)) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(distribute,[status(thm)],[62]) ).
cnf(64,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[63]) ).
cnf(66,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[63]) ).
fof(102,plain,
! [X3,X1] :
( ( ~ member(X3,power_set(X1))
| subset(X3,X1) )
& ( ~ subset(X3,X1)
| member(X3,power_set(X1)) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(103,plain,
! [X4,X5] :
( ( ~ member(X4,power_set(X5))
| subset(X4,X5) )
& ( ~ subset(X4,X5)
| member(X4,power_set(X5)) ) ),
inference(variable_rename,[status(thm)],[102]) ).
cnf(104,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[103]) ).
fof(106,negated_conjecture,
? [X1] :
( member(X1,on)
& ~ equal_set(X1,intersection(X1,power_set(X1))) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(107,negated_conjecture,
? [X2] :
( member(X2,on)
& ~ equal_set(X2,intersection(X2,power_set(X2))) ),
inference(variable_rename,[status(thm)],[106]) ).
fof(108,negated_conjecture,
( member(esk12_0,on)
& ~ equal_set(esk12_0,intersection(esk12_0,power_set(esk12_0))) ),
inference(skolemize,[status(esa)],[107]) ).
cnf(109,negated_conjecture,
~ equal_set(esk12_0,intersection(esk12_0,power_set(esk12_0))),
inference(split_conjunct,[status(thm)],[108]) ).
cnf(110,negated_conjecture,
member(esk12_0,on),
inference(split_conjunct,[status(thm)],[108]) ).
cnf(116,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ member(X2,on)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[20,30,theory(equality)]) ).
cnf(121,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[66,19,theory(equality)]) ).
cnf(125,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[18,64,theory(equality)]) ).
cnf(127,negated_conjecture,
( ~ subset(intersection(esk12_0,power_set(esk12_0)),esk12_0)
| ~ subset(esk12_0,intersection(esk12_0,power_set(esk12_0))) ),
inference(spm,[status(thm)],[109,48,theory(equality)]) ).
cnf(244,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[18,121,theory(equality)]) ).
cnf(247,negated_conjecture,
( $false
| ~ subset(esk12_0,intersection(esk12_0,power_set(esk12_0))) ),
inference(rw,[status(thm)],[127,244,theory(equality)]) ).
cnf(248,negated_conjecture,
~ subset(esk12_0,intersection(esk12_0,power_set(esk12_0))),
inference(cn,[status(thm)],[247,theory(equality)]) ).
cnf(251,negated_conjecture,
( member(X1,esk12_0)
| ~ member(X1,X2)
| ~ member(X2,esk12_0) ),
inference(spm,[status(thm)],[116,110,theory(equality)]) ).
cnf(263,negated_conjecture,
( member(X1,esk12_0)
| subset(esk12_0,X2)
| ~ member(X1,esk1_2(esk12_0,X2)) ),
inference(spm,[status(thm)],[251,19,theory(equality)]) ).
cnf(275,negated_conjecture,
( member(esk1_2(esk1_2(esk12_0,X1),X2),esk12_0)
| subset(esk12_0,X1)
| subset(esk1_2(esk12_0,X1),X2) ),
inference(spm,[status(thm)],[263,19,theory(equality)]) ).
cnf(347,plain,
( subset(X1,intersection(X2,power_set(X3)))
| ~ member(esk1_2(X1,intersection(X2,power_set(X3))),X2)
| ~ subset(esk1_2(X1,intersection(X2,power_set(X3))),X3) ),
inference(spm,[status(thm)],[125,104,theory(equality)]) ).
cnf(4325,negated_conjecture,
( subset(esk1_2(esk12_0,X1),esk12_0)
| subset(esk12_0,X1) ),
inference(spm,[status(thm)],[18,275,theory(equality)]) ).
cnf(11933,plain,
( subset(X1,intersection(X1,power_set(X2)))
| ~ subset(esk1_2(X1,intersection(X1,power_set(X2))),X2) ),
inference(spm,[status(thm)],[347,19,theory(equality)]) ).
cnf(805838,negated_conjecture,
subset(esk12_0,intersection(esk12_0,power_set(esk12_0))),
inference(spm,[status(thm)],[11933,4325,theory(equality)]) ).
cnf(805892,negated_conjecture,
$false,
inference(sr,[status(thm)],[805838,248,theory(equality)]) ).
cnf(805893,negated_conjecture,
$false,
805892,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET812+4.p
% --creating new selector for [SET006+0.ax, SET006+4.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpOf_kV2/sel_SET812+4.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpOf_kV2/sel_SET812+4.p_2 with time limit 81
% -prover status Theorem
% Problem SET812+4.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET812+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET812+4.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
%
%------------------------------------------------------------------------------