TSTP Solution File: SET941+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET941+1 : TPTP v5.0.0. Released v3.2.0.
% 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 03:49:19 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 4 unt; 0 def)
% Number of atoms : 166 ( 17 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 205 ( 74 ~; 83 |; 40 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 56 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/tmp/tmpNE3Anv/sel_SET941+1.p_1',d4_tarski) ).
fof(3,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> subset(X3,X2) )
=> subset(union(X1),X2) ),
file('/tmp/tmpNE3Anv/sel_SET941+1.p_1',t94_zfmisc_1) ).
fof(6,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpNE3Anv/sel_SET941+1.p_1',d3_tarski) ).
fof(8,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> subset(X3,X2) )
=> subset(union(X1),X2) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(11,plain,
! [X1,X2] :
( ( X2 != union(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4] :
( in(X3,X4)
& in(X4,X1) ) )
& ( ! [X4] :
( ~ in(X3,X4)
| ~ in(X4,X1) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4] :
( ~ in(X3,X4)
| ~ in(X4,X1) ) )
& ( in(X3,X2)
| ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) )
| X2 = union(X1) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(12,plain,
! [X5,X6] :
( ( X6 != union(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ? [X8] :
( in(X7,X8)
& in(X8,X5) ) )
& ( ! [X9] :
( ~ in(X7,X9)
| ~ in(X9,X5) )
| in(X7,X6) ) ) )
& ( ? [X10] :
( ( ~ in(X10,X6)
| ! [X11] :
( ~ in(X10,X11)
| ~ in(X11,X5) ) )
& ( in(X10,X6)
| ? [X12] :
( in(X10,X12)
& in(X12,X5) ) ) )
| X6 = union(X5) ) ),
inference(variable_rename,[status(thm)],[11]) ).
fof(13,plain,
! [X5,X6] :
( ( X6 != union(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ( in(X7,esk1_3(X5,X6,X7))
& in(esk1_3(X5,X6,X7),X5) ) )
& ( ! [X9] :
( ~ in(X7,X9)
| ~ in(X9,X5) )
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk2_2(X5,X6),X6)
| ! [X11] :
( ~ in(esk2_2(X5,X6),X11)
| ~ in(X11,X5) ) )
& ( in(esk2_2(X5,X6),X6)
| ( in(esk2_2(X5,X6),esk3_2(X5,X6))
& in(esk3_2(X5,X6),X5) ) ) )
| X6 = union(X5) ) ),
inference(skolemize,[status(esa)],[12]) ).
fof(14,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ~ in(esk2_2(X5,X6),X11)
| ~ in(X11,X5)
| ~ in(esk2_2(X5,X6),X6) )
& ( in(esk2_2(X5,X6),X6)
| ( in(esk2_2(X5,X6),esk3_2(X5,X6))
& in(esk3_2(X5,X6),X5) ) ) )
| X6 = union(X5) )
& ( ( ( ~ in(X7,X9)
| ~ in(X9,X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| ( in(X7,esk1_3(X5,X6,X7))
& in(esk1_3(X5,X6,X7),X5) ) ) )
| X6 != union(X5) ) ),
inference(shift_quantors,[status(thm)],[13]) ).
fof(15,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(esk2_2(X5,X6),X11)
| ~ in(X11,X5)
| ~ in(esk2_2(X5,X6),X6)
| X6 = union(X5) )
& ( in(esk2_2(X5,X6),esk3_2(X5,X6))
| in(esk2_2(X5,X6),X6)
| X6 = union(X5) )
& ( in(esk3_2(X5,X6),X5)
| in(esk2_2(X5,X6),X6)
| X6 = union(X5) )
& ( ~ in(X7,X9)
| ~ in(X9,X5)
| in(X7,X6)
| X6 != union(X5) )
& ( in(X7,esk1_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk1_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) ) ),
inference(distribute,[status(thm)],[14]) ).
cnf(16,plain,
( in(esk1_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,plain,
( in(X3,esk1_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(25,negated_conjecture,
? [X1,X2] :
( ! [X3] :
( ~ in(X3,X1)
| subset(X3,X2) )
& ~ subset(union(X1),X2) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(26,negated_conjecture,
? [X4,X5] :
( ! [X6] :
( ~ in(X6,X4)
| subset(X6,X5) )
& ~ subset(union(X4),X5) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,negated_conjecture,
( ! [X6] :
( ~ in(X6,esk5_0)
| subset(X6,esk6_0) )
& ~ subset(union(esk5_0),esk6_0) ),
inference(skolemize,[status(esa)],[26]) ).
fof(28,negated_conjecture,
! [X6] :
( ( ~ in(X6,esk5_0)
| subset(X6,esk6_0) )
& ~ subset(union(esk5_0),esk6_0) ),
inference(shift_quantors,[status(thm)],[27]) ).
cnf(29,negated_conjecture,
~ subset(union(esk5_0),esk6_0),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,negated_conjecture,
( subset(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(37,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(38,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk8_2(X4,X5),X4)
& ~ in(esk8_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[38]) ).
fof(40,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk8_2(X4,X5),X4)
& ~ in(esk8_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[39]) ).
fof(41,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk8_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk8_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(42,plain,
( subset(X1,X2)
| ~ in(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,plain,
( subset(X1,X2)
| in(esk8_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(44,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(53,plain,
( in(X1,esk1_3(X2,union(X2),X1))
| ~ in(X1,union(X2)) ),
inference(er,[status(thm)],[17,theory(equality)]) ).
cnf(54,plain,
( in(esk1_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[16,theory(equality)]) ).
cnf(72,plain,
( in(esk8_2(union(X1),X2),esk1_3(X1,union(X1),esk8_2(union(X1),X2)))
| subset(union(X1),X2) ),
inference(spm,[status(thm)],[53,43,theory(equality)]) ).
cnf(75,plain,
( in(esk1_3(X1,union(X1),esk8_2(union(X1),X2)),X1)
| subset(union(X1),X2) ),
inference(spm,[status(thm)],[54,43,theory(equality)]) ).
cnf(92,negated_conjecture,
( subset(esk1_3(esk5_0,union(esk5_0),esk8_2(union(esk5_0),X1)),esk6_0)
| subset(union(esk5_0),X1) ),
inference(spm,[status(thm)],[30,75,theory(equality)]) ).
cnf(100,negated_conjecture,
( in(X1,esk6_0)
| subset(union(esk5_0),X2)
| ~ in(X1,esk1_3(esk5_0,union(esk5_0),esk8_2(union(esk5_0),X2))) ),
inference(spm,[status(thm)],[44,92,theory(equality)]) ).
cnf(172,negated_conjecture,
( subset(union(esk5_0),X1)
| in(esk8_2(union(esk5_0),X1),esk6_0) ),
inference(spm,[status(thm)],[100,72,theory(equality)]) ).
cnf(175,negated_conjecture,
subset(union(esk5_0),esk6_0),
inference(spm,[status(thm)],[42,172,theory(equality)]) ).
cnf(178,negated_conjecture,
$false,
inference(sr,[status(thm)],[175,29,theory(equality)]) ).
cnf(179,negated_conjecture,
$false,
178,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET941+1.p
% --creating new selector for []
% -running prover on /tmp/tmpNE3Anv/sel_SET941+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET941+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET941+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET941+1.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
%
%------------------------------------------------------------------------------