TSTP Solution File: SET636+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET636+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 03:06:18 EST 2010
% Result : Theorem 3.69s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 11 unt; 0 def)
% Number of atoms : 197 ( 31 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 232 ( 92 ~; 94 |; 38 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 3 sgn 62 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpGjZVYn/sel_SET636+3.p_1',intersect_defn) ).
fof(7,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/tmp/tmpGjZVYn/sel_SET636+3.p_1',equal_member_defn) ).
fof(8,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/tmp/tmpGjZVYn/sel_SET636+3.p_1',disjoint_defn) ).
fof(9,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
file('/tmp/tmpGjZVYn/sel_SET636+3.p_1',prove_th118) ).
fof(10,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpGjZVYn/sel_SET636+3.p_1',intersection_defn) ).
fof(12,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpGjZVYn/sel_SET636+3.p_1',empty_set_defn) ).
fof(13,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> intersection(X1,X2) = empty_set ),
inference(assume_negation,[status(cth)],[9]) ).
fof(15,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[8,theory(equality)]) ).
fof(16,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(39,plain,
! [X1,X2] :
( ( ~ intersect(X1,X2)
| ? [X3] :
( member(X3,X1)
& member(X3,X2) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X2) )
| intersect(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(40,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ? [X6] :
( member(X6,X4)
& member(X6,X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(variable_rename,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ( member(esk3_2(X4,X5),X4)
& member(esk3_2(X4,X5),X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( ~ intersect(X4,X5)
| ( member(esk3_2(X4,X5),X4)
& member(esk3_2(X4,X5),X5) ) ) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( member(esk3_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk3_2(X4,X5),X5)
| ~ intersect(X4,X5) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(44,plain,
( member(esk3_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(45,plain,
( member(esk3_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
cnf(46,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(50,plain,
! [X1,X2] :
( ( X1 != X2
| ! [X3] :
( ( ~ member(X3,X1)
| member(X3,X2) )
& ( ~ member(X3,X2)
| member(X3,X1) ) ) )
& ( ? [X3] :
( ( ~ member(X3,X1)
| ~ member(X3,X2) )
& ( member(X3,X1)
| member(X3,X2) ) )
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(51,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ? [X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5) )
& ( member(X7,X4)
| member(X7,X5) ) )
| X4 = X5 ) ),
inference(variable_rename,[status(thm)],[50]) ).
fof(52,plain,
! [X4,X5] :
( ( X4 != X5
| ! [X6] :
( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) ) )
& ( ( ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5) )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(skolemize,[status(esa)],[51]) ).
fof(53,plain,
! [X4,X5,X6] :
( ( ( ( ~ member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X5)
| member(X6,X4) ) )
| X4 != X5 )
& ( ( ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5) )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5) ) )
| X4 = X5 ) ),
inference(shift_quantors,[status(thm)],[52]) ).
fof(54,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| X4 != X5 )
& ( ~ member(X6,X5)
| member(X6,X4)
| X4 != X5 )
& ( ~ member(esk4_2(X4,X5),X4)
| ~ member(esk4_2(X4,X5),X5)
| X4 = X5 )
& ( member(esk4_2(X4,X5),X4)
| member(esk4_2(X4,X5),X5)
| X4 = X5 ) ),
inference(distribute,[status(thm)],[53]) ).
cnf(55,plain,
( X1 = X2
| member(esk4_2(X1,X2),X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[54]) ).
fof(59,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) )
& ( intersect(X1,X2)
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(60,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| ~ intersect(X3,X4) )
& ( intersect(X3,X4)
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[59]) ).
cnf(61,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
cnf(62,plain,
( ~ intersect(X1,X2)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[60]) ).
fof(63,negated_conjecture,
? [X1,X2] :
( ( ~ disjoint(X1,X2)
| intersection(X1,X2) != empty_set )
& ( disjoint(X1,X2)
| intersection(X1,X2) = empty_set ) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(64,negated_conjecture,
? [X3,X4] :
( ( ~ disjoint(X3,X4)
| intersection(X3,X4) != empty_set )
& ( disjoint(X3,X4)
| intersection(X3,X4) = empty_set ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,negated_conjecture,
( ( ~ disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) != empty_set )
& ( disjoint(esk5_0,esk6_0)
| intersection(esk5_0,esk6_0) = empty_set ) ),
inference(skolemize,[status(esa)],[64]) ).
cnf(66,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(67,negated_conjecture,
( intersection(esk5_0,esk6_0) != empty_set
| ~ disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(68,plain,
! [X1,X2,X3] :
( ( ~ 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)],[10]) ).
fof(69,plain,
! [X4,X5,X6] :
( ( ~ member(X6,intersection(X4,X5))
| ( member(X6,X4)
& member(X6,X5) ) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[68]) ).
fof(70,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[69]) ).
cnf(71,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[70]) ).
cnf(72,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[70]) ).
cnf(73,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[70]) ).
fof(76,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[16]) ).
cnf(77,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(86,negated_conjecture,
( intersection(esk5_0,esk6_0) = empty_set
| ~ intersect(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[62,66,theory(equality)]) ).
cnf(122,plain,
( empty_set = X1
| member(esk4_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[77,55,theory(equality)]) ).
cnf(147,plain,
( member(esk4_2(empty_set,intersection(X1,X2)),X2)
| empty_set = intersection(X1,X2) ),
inference(spm,[status(thm)],[72,122,theory(equality)]) ).
cnf(148,plain,
( member(esk4_2(empty_set,intersection(X1,X2)),X1)
| empty_set = intersection(X1,X2) ),
inference(spm,[status(thm)],[73,122,theory(equality)]) ).
cnf(162,plain,
( intersect(X1,X2)
| intersection(X3,X2) = empty_set
| ~ member(esk4_2(empty_set,intersection(X3,X2)),X1) ),
inference(spm,[status(thm)],[46,147,theory(equality)]) ).
cnf(1585,plain,
( intersection(X1,X2) = empty_set
| intersect(X1,X2) ),
inference(spm,[status(thm)],[162,148,theory(equality)]) ).
cnf(1607,negated_conjecture,
intersection(esk5_0,esk6_0) = empty_set,
inference(spm,[status(thm)],[86,1585,theory(equality)]) ).
cnf(1622,negated_conjecture,
( member(X1,empty_set)
| ~ member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[71,1607,theory(equality)]) ).
cnf(1667,negated_conjecture,
( $false
| ~ disjoint(esk5_0,esk6_0) ),
inference(rw,[status(thm)],[67,1607,theory(equality)]) ).
cnf(1668,negated_conjecture,
~ disjoint(esk5_0,esk6_0),
inference(cn,[status(thm)],[1667,theory(equality)]) ).
cnf(1672,negated_conjecture,
( ~ member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(sr,[status(thm)],[1622,77,theory(equality)]) ).
cnf(1697,negated_conjecture,
intersect(esk5_0,esk6_0),
inference(spm,[status(thm)],[1668,61,theory(equality)]) ).
cnf(1787,negated_conjecture,
( ~ member(esk3_2(X1,esk6_0),esk5_0)
| ~ intersect(X1,esk6_0) ),
inference(spm,[status(thm)],[1672,44,theory(equality)]) ).
cnf(143606,negated_conjecture,
~ intersect(esk5_0,esk6_0),
inference(spm,[status(thm)],[1787,45,theory(equality)]) ).
cnf(143617,negated_conjecture,
$false,
inference(rw,[status(thm)],[143606,1697,theory(equality)]) ).
cnf(143618,negated_conjecture,
$false,
inference(cn,[status(thm)],[143617,theory(equality)]) ).
cnf(143619,negated_conjecture,
$false,
143618,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET636+3.p
% --creating new selector for []
% -running prover on /tmp/tmpGjZVYn/sel_SET636+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET636+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET636+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET636+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
%
%------------------------------------------------------------------------------