TSTP Solution File: SET696+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET696+4 : 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 03:12:34 EST 2010
% Result : Theorem 0.30s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 167 ( 67 ~; 57 |; 35 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 7 sgn 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpeww8Lv/sel_SET696+4.p_1',subset) ).
fof(2,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpeww8Lv/sel_SET696+4.p_1',equal_set) ).
fof(3,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpeww8Lv/sel_SET696+4.p_1',intersection) ).
fof(4,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/tmp/tmpeww8Lv/sel_SET696+4.p_1',difference) ).
fof(5,axiom,
! [X3] : ~ member(X3,empty_set),
file('/tmp/tmpeww8Lv/sel_SET696+4.p_1',empty_set) ).
fof(6,conjecture,
! [X1,X4] :
( subset(X1,X4)
=> equal_set(intersection(difference(X4,X1),X1),empty_set) ),
file('/tmp/tmpeww8Lv/sel_SET696+4.p_1',thI28) ).
fof(7,negated_conjecture,
~ ! [X1,X4] :
( subset(X1,X4)
=> equal_set(intersection(difference(X4,X1),X1),empty_set) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(8,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).
fof(9,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(10,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(11,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)],[10]) ).
fof(12,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)],[11]) ).
fof(13,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)],[12]) ).
fof(14,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)],[13]) ).
cnf(16,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,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)],[2]) ).
fof(19,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)],[18]) ).
fof(20,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)],[19]) ).
cnf(21,plain,
( equal_set(X1,X2)
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(24,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)],[3]) ).
fof(25,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)],[24]) ).
fof(26,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)],[25]) ).
cnf(28,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[26]) ).
cnf(29,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[26]) ).
fof(30,plain,
! [X2,X1,X4] :
( ( ~ member(X2,difference(X4,X1))
| ( member(X2,X4)
& ~ member(X2,X1) ) )
& ( ~ member(X2,X4)
| member(X2,X1)
| member(X2,difference(X4,X1)) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(31,plain,
! [X5,X6,X7] :
( ( ~ member(X5,difference(X7,X6))
| ( member(X5,X7)
& ~ member(X5,X6) ) )
& ( ~ member(X5,X7)
| member(X5,X6)
| member(X5,difference(X7,X6)) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X5,X6,X7] :
( ( member(X5,X7)
| ~ member(X5,difference(X7,X6)) )
& ( ~ member(X5,X6)
| ~ member(X5,difference(X7,X6)) )
& ( ~ member(X5,X7)
| member(X5,X6)
| member(X5,difference(X7,X6)) ) ),
inference(distribute,[status(thm)],[31]) ).
cnf(34,plain,
( ~ member(X1,difference(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[32]) ).
fof(36,plain,
! [X4] : ~ member(X4,empty_set),
inference(variable_rename,[status(thm)],[9]) ).
cnf(37,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[36]) ).
fof(38,negated_conjecture,
? [X1,X4] :
( subset(X1,X4)
& ~ equal_set(intersection(difference(X4,X1),X1),empty_set) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(39,negated_conjecture,
? [X5,X6] :
( subset(X5,X6)
& ~ equal_set(intersection(difference(X6,X5),X5),empty_set) ),
inference(variable_rename,[status(thm)],[38]) ).
fof(40,negated_conjecture,
( subset(esk2_0,esk3_0)
& ~ equal_set(intersection(difference(esk3_0,esk2_0),esk2_0),empty_set) ),
inference(skolemize,[status(esa)],[39]) ).
cnf(41,negated_conjecture,
~ equal_set(intersection(difference(esk3_0,esk2_0),esk2_0),empty_set),
inference(split_conjunct,[status(thm)],[40]) ).
cnf(45,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[37,16,theory(equality)]) ).
cnf(47,negated_conjecture,
( ~ subset(empty_set,intersection(difference(esk3_0,esk2_0),esk2_0))
| ~ subset(intersection(difference(esk3_0,esk2_0),esk2_0),empty_set) ),
inference(spm,[status(thm)],[41,21,theory(equality)]) ).
cnf(49,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[28,16,theory(equality)]) ).
cnf(50,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[29,16,theory(equality)]) ).
cnf(61,negated_conjecture,
( $false
| ~ subset(intersection(difference(esk3_0,esk2_0),esk2_0),empty_set) ),
inference(rw,[status(thm)],[47,45,theory(equality)]) ).
cnf(62,negated_conjecture,
~ subset(intersection(difference(esk3_0,esk2_0),esk2_0),empty_set),
inference(cn,[status(thm)],[61,theory(equality)]) ).
cnf(88,plain,
( subset(intersection(difference(X1,X2),X3),X4)
| ~ member(esk1_2(intersection(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[34,50,theory(equality)]) ).
cnf(1001,plain,
subset(intersection(difference(X1,X2),X2),X3),
inference(spm,[status(thm)],[88,49,theory(equality)]) ).
cnf(1015,negated_conjecture,
$false,
inference(rw,[status(thm)],[62,1001,theory(equality)]) ).
cnf(1016,negated_conjecture,
$false,
inference(cn,[status(thm)],[1015,theory(equality)]) ).
cnf(1017,negated_conjecture,
$false,
1016,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET696+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpeww8Lv/sel_SET696+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET696+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET696+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET696+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
%
%------------------------------------------------------------------------------