TSTP Solution File: SET162+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET162+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 02:52:55 EST 2010
% Result : Theorem 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 20 unt; 0 def)
% Number of atoms : 121 ( 22 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 128 ( 51 ~; 50 |; 23 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 3 sgn 47 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1] : union(X1,empty_set) = X1,
file('/tmp/tmpaZuS2N/sel_SET162+3.p_1',prove_union_empty_set) ).
fof(2,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpaZuS2N/sel_SET162+3.p_1',commutativity_of_union) ).
fof(4,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpaZuS2N/sel_SET162+3.p_1',equal_defn) ).
fof(5,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpaZuS2N/sel_SET162+3.p_1',union_defn) ).
fof(6,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpaZuS2N/sel_SET162+3.p_1',subset_defn) ).
fof(9,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmpaZuS2N/sel_SET162+3.p_1',empty_set_defn) ).
fof(10,negated_conjecture,
~ ! [X1] : union(X1,empty_set) = X1,
inference(assume_negation,[status(cth)],[1]) ).
fof(12,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(13,negated_conjecture,
? [X1] : union(X1,empty_set) != X1,
inference(fof_nnf,[status(thm)],[10]) ).
fof(14,negated_conjecture,
? [X2] : union(X2,empty_set) != X2,
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
union(esk1_0,empty_set) != esk1_0,
inference(skolemize,[status(esa)],[14]) ).
cnf(16,negated_conjecture,
union(esk1_0,empty_set) != esk1_0,
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(18,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[17]) ).
fof(25,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(26,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(31,plain,
! [X1,X2,X3] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(32,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ( ~ member(X6,X4)
& ~ member(X6,X5) )
| member(X6,union(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[32]) ).
cnf(34,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[33]) ).
cnf(36,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(37,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)],[6]) ).
fof(38,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)],[37]) ).
fof(39,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk3_2(X4,X5),X4)
& ~ member(esk3_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk3_2(X4,X5),X4)
& ~ member(esk3_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk3_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk3_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(42,plain,
( subset(X1,X2)
| ~ member(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,plain,
( subset(X1,X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(56,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[12]) ).
cnf(57,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,negated_conjecture,
union(empty_set,esk1_0) != esk1_0,
inference(rw,[status(thm)],[16,18,theory(equality)]) ).
cnf(73,plain,
( subset(X1,union(X2,X3))
| ~ member(esk3_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[42,34,theory(equality)]) ).
cnf(83,plain,
( member(esk3_2(union(X1,X2),X3),X2)
| member(esk3_2(union(X1,X2),X3),X1)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[36,43,theory(equality)]) ).
cnf(122,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[73,43,theory(equality)]) ).
cnf(245,plain,
( subset(union(empty_set,X1),X2)
| member(esk3_2(union(empty_set,X1),X2),X1) ),
inference(spm,[status(thm)],[57,83,theory(equality)]) ).
cnf(3911,plain,
subset(union(empty_set,X1),X1),
inference(spm,[status(thm)],[42,245,theory(equality)]) ).
cnf(3952,plain,
( X1 = union(empty_set,X1)
| ~ subset(X1,union(empty_set,X1)) ),
inference(spm,[status(thm)],[28,3911,theory(equality)]) ).
cnf(3969,plain,
( X1 = union(empty_set,X1)
| $false ),
inference(rw,[status(thm)],[3952,122,theory(equality)]) ).
cnf(3970,plain,
X1 = union(empty_set,X1),
inference(cn,[status(thm)],[3969,theory(equality)]) ).
cnf(4040,negated_conjecture,
$false,
inference(rw,[status(thm)],[58,3970,theory(equality)]) ).
cnf(4041,negated_conjecture,
$false,
inference(cn,[status(thm)],[4040,theory(equality)]) ).
cnf(4042,negated_conjecture,
$false,
4041,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET162+3.p
% --creating new selector for []
% -running prover on /tmp/tmpaZuS2N/sel_SET162+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET162+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET162+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET162+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
%
%------------------------------------------------------------------------------