TSTP Solution File: SET945+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET945+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 03:49:54 EST 2010
% Result : Theorem 3.08s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 3 unt; 0 def)
% Number of atoms : 267 ( 40 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 357 ( 141 ~; 141 |; 66 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 158 ( 5 sgn 86 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',symmetry_r1_xboole_0) ).
fof(5,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',d4_tarski) ).
fof(6,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> disjoint(X3,X2) )
=> disjoint(union(X1),X2) ),
file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',t98_zfmisc_1) ).
fof(8,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',d3_xboole_0) ).
fof(10,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/tmp/tmpb-6oXC/sel_SET945+1.p_1',t4_xboole_0) ).
fof(11,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> disjoint(X3,X2) )
=> disjoint(union(X1),X2) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(14,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(19,plain,
! [X1,X2] :
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(20,plain,
! [X3,X4] :
( ~ disjoint(X3,X4)
| disjoint(X4,X3) ),
inference(variable_rename,[status(thm)],[19]) ).
cnf(21,plain,
( disjoint(X1,X2)
| ~ disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(25,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)],[5]) ).
fof(26,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)],[25]) ).
fof(27,plain,
! [X5,X6] :
( ( X6 != union(X5)
| ! [X7] :
( ( ~ in(X7,X6)
| ( in(X7,esk2_3(X5,X6,X7))
& in(esk2_3(X5,X6,X7),X5) ) )
& ( ! [X9] :
( ~ in(X7,X9)
| ~ in(X9,X5) )
| in(X7,X6) ) ) )
& ( ( ( ~ in(esk3_2(X5,X6),X6)
| ! [X11] :
( ~ in(esk3_2(X5,X6),X11)
| ~ in(X11,X5) ) )
& ( in(esk3_2(X5,X6),X6)
| ( in(esk3_2(X5,X6),esk4_2(X5,X6))
& in(esk4_2(X5,X6),X5) ) ) )
| X6 = union(X5) ) ),
inference(skolemize,[status(esa)],[26]) ).
fof(28,plain,
! [X5,X6,X7,X9,X11] :
( ( ( ( ~ in(esk3_2(X5,X6),X11)
| ~ in(X11,X5)
| ~ in(esk3_2(X5,X6),X6) )
& ( in(esk3_2(X5,X6),X6)
| ( in(esk3_2(X5,X6),esk4_2(X5,X6))
& in(esk4_2(X5,X6),X5) ) ) )
| X6 = union(X5) )
& ( ( ( ~ in(X7,X9)
| ~ in(X9,X5)
| in(X7,X6) )
& ( ~ in(X7,X6)
| ( in(X7,esk2_3(X5,X6,X7))
& in(esk2_3(X5,X6,X7),X5) ) ) )
| X6 != union(X5) ) ),
inference(shift_quantors,[status(thm)],[27]) ).
fof(29,plain,
! [X5,X6,X7,X9,X11] :
( ( ~ in(esk3_2(X5,X6),X11)
| ~ in(X11,X5)
| ~ in(esk3_2(X5,X6),X6)
| X6 = union(X5) )
& ( in(esk3_2(X5,X6),esk4_2(X5,X6))
| in(esk3_2(X5,X6),X6)
| X6 = union(X5) )
& ( in(esk4_2(X5,X6),X5)
| in(esk3_2(X5,X6),X6)
| X6 = union(X5) )
& ( ~ in(X7,X9)
| ~ in(X9,X5)
| in(X7,X6)
| X6 != union(X5) )
& ( in(X7,esk2_3(X5,X6,X7))
| ~ in(X7,X6)
| X6 != union(X5) )
& ( in(esk2_3(X5,X6,X7),X5)
| ~ in(X7,X6)
| X6 != union(X5) ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(30,plain,
( in(esk2_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(31,plain,
( in(X3,esk2_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(36,negated_conjecture,
? [X1,X2] :
( ! [X3] :
( ~ in(X3,X1)
| disjoint(X3,X2) )
& ~ disjoint(union(X1),X2) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(37,negated_conjecture,
? [X4,X5] :
( ! [X6] :
( ~ in(X6,X4)
| disjoint(X6,X5) )
& ~ disjoint(union(X4),X5) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,negated_conjecture,
( ! [X6] :
( ~ in(X6,esk5_0)
| disjoint(X6,esk6_0) )
& ~ disjoint(union(esk5_0),esk6_0) ),
inference(skolemize,[status(esa)],[37]) ).
fof(39,negated_conjecture,
! [X6] :
( ( ~ in(X6,esk5_0)
| disjoint(X6,esk6_0) )
& ~ disjoint(union(esk5_0),esk6_0) ),
inference(shift_quantors,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
~ disjoint(union(esk5_0),esk6_0),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(41,negated_conjecture,
( disjoint(X1,esk6_0)
| ~ in(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(45,plain,
! [X1,X2,X3] :
( ( X3 != set_intersection2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) ) )
| X3 = set_intersection2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(46,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| ~ in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& in(X9,X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ~ in(esk8_3(X5,X6,X7),X5)
| ~ in(esk8_3(X5,X6,X7),X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| ( in(esk8_3(X5,X6,X7),X5)
& in(esk8_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[46]) ).
fof(48,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) )
| X7 != set_intersection2(X5,X6) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ~ in(esk8_3(X5,X6,X7),X5)
| ~ in(esk8_3(X5,X6,X7),X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| ( in(esk8_3(X5,X6,X7),X5)
& in(esk8_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[47]) ).
fof(49,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk8_3(X5,X6,X7),X7)
| ~ in(esk8_3(X5,X6,X7),X5)
| ~ in(esk8_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X5)
| in(esk8_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X6)
| in(esk8_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[48]) ).
cnf(53,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(54,plain,
( in(X4,X3)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(55,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(59,plain,
! [X1,X2] :
( ( disjoint(X1,X2)
| ? [X3] : in(X3,set_intersection2(X1,X2)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(60,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| ? [X6] : in(X6,set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(variable_rename,[status(thm)],[59]) ).
fof(61,plain,
! [X4,X5] :
( ( disjoint(X4,X5)
| in(esk9_2(X4,X5),set_intersection2(X4,X5)) )
& ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) ) ),
inference(skolemize,[status(esa)],[60]) ).
fof(62,plain,
! [X4,X5,X7] :
( ( ~ in(X7,set_intersection2(X4,X5))
| ~ disjoint(X4,X5) )
& ( disjoint(X4,X5)
| in(esk9_2(X4,X5),set_intersection2(X4,X5)) ) ),
inference(shift_quantors,[status(thm)],[61]) ).
cnf(63,plain,
( in(esk9_2(X1,X2),set_intersection2(X1,X2))
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(64,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[62]) ).
cnf(66,negated_conjecture,
( disjoint(esk6_0,X1)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[21,41,theory(equality)]) ).
cnf(71,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[54,theory(equality)]) ).
cnf(79,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[55,theory(equality)]) ).
cnf(95,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[53,theory(equality)]) ).
cnf(135,plain,
( in(esk9_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[71,63,theory(equality)]) ).
cnf(178,plain,
( in(esk9_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[79,63,theory(equality)]) ).
cnf(274,plain,
( ~ disjoint(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[64,95,theory(equality)]) ).
cnf(284,plain,
( ~ in(X1,X4)
| ~ disjoint(X4,esk2_3(X2,X3,X1))
| union(X2) != X3
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[274,31,theory(equality)]) ).
cnf(4185,negated_conjecture,
( union(X1) != X2
| ~ in(X3,esk6_0)
| ~ in(X3,X2)
| ~ in(esk2_3(X1,X2,X3),esk5_0) ),
inference(spm,[status(thm)],[284,66,theory(equality)]) ).
cnf(53348,negated_conjecture,
( union(esk5_0) != X1
| ~ in(X2,esk6_0)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[4185,30,theory(equality)]) ).
cnf(53363,negated_conjecture,
( disjoint(X2,esk6_0)
| union(esk5_0) != X1
| ~ in(esk9_2(X2,esk6_0),X1) ),
inference(spm,[status(thm)],[53348,135,theory(equality)]) ).
cnf(53494,negated_conjecture,
( disjoint(X1,esk6_0)
| union(esk5_0) != X1 ),
inference(spm,[status(thm)],[53363,178,theory(equality)]) ).
cnf(53930,negated_conjecture,
$false,
inference(spm,[status(thm)],[40,53494,theory(equality)]) ).
cnf(54140,negated_conjecture,
$false,
53930,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET945+1.p
% --creating new selector for []
% -running prover on /tmp/tmpb-6oXC/sel_SET945+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET945+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET945+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET945+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
%
%------------------------------------------------------------------------------