TSTP Solution File: SET920+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET920+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 03:47:27 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 192 ( 86 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 248 ( 88 ~; 100 |; 54 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 5 sgn 58 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',commutativity_k3_xboole_0) ).
fof(6,conjecture,
! [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
=> in(X1,X3) ),
file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',t63_zfmisc_1) ).
fof(7,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',d3_xboole_0) ).
fof(9,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmp7s5L5w/sel_SET920+1.p_1',d2_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
=> in(X1,X3) ),
inference(assume_negation,[status(cth)],[6]) ).
fof(13,plain,
! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(14,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[13]) ).
fof(25,negated_conjecture,
? [X1,X2,X3] :
( set_intersection2(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
& ~ in(X1,X3) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(26,negated_conjecture,
? [X4,X5,X6] :
( set_intersection2(unordered_pair(X4,X5),X6) = unordered_pair(X4,X5)
& ~ in(X4,X6) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,negated_conjecture,
( set_intersection2(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0)
& ~ in(esk3_0,esk5_0) ),
inference(skolemize,[status(esa)],[26]) ).
cnf(28,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[27]) ).
cnf(29,negated_conjecture,
set_intersection2(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[27]) ).
fof(30,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)],[7]) ).
fof(31,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)],[30]) ).
fof(32,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(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,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(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6) )
& ( in(esk6_3(X5,X6,X7),X7)
| ( in(esk6_3(X5,X6,X7),X5)
& in(esk6_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,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(esk6_3(X5,X6,X7),X7)
| ~ in(esk6_3(X5,X6,X7),X5)
| ~ in(esk6_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X5)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk6_3(X5,X6,X7),X6)
| in(esk6_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(40,plain,
( in(X4,X2)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(44,plain,
! [X1,X2,X3] :
( ( X3 != unordered_pair(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| X4 = X1
| X4 = X2 )
& ( ( X4 != X1
& X4 != X2 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( X4 != X1
& X4 != X2 ) )
& ( in(X4,X3)
| X4 = X1
| X4 = X2 ) )
| X3 = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(45,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( X9 != X5
& X9 != X6 ) )
& ( in(X9,X7)
| X9 = X5
| X9 = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[44]) ).
fof(46,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
| ( esk7_3(X5,X6,X7) != X5
& esk7_3(X5,X6,X7) != X6 ) )
& ( in(esk7_3(X5,X6,X7),X7)
| esk7_3(X5,X6,X7) = X5
| esk7_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[45]) ).
fof(47,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) )
| X7 != unordered_pair(X5,X6) )
& ( ( ( ~ in(esk7_3(X5,X6,X7),X7)
| ( esk7_3(X5,X6,X7) != X5
& esk7_3(X5,X6,X7) != X6 ) )
& ( in(esk7_3(X5,X6,X7),X7)
| esk7_3(X5,X6,X7) = X5
| esk7_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk7_3(X5,X6,X7) != X5
| ~ in(esk7_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk7_3(X5,X6,X7) != X6
| ~ in(esk7_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk7_3(X5,X6,X7),X7)
| esk7_3(X5,X6,X7) = X5
| esk7_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(53,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X2 ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(57,negated_conjecture,
set_intersection2(esk5_0,unordered_pair(esk3_0,esk4_0)) = unordered_pair(esk3_0,esk4_0),
inference(rw,[status(thm)],[29,14,theory(equality)]) ).
cnf(61,plain,
( in(X1,X2)
| unordered_pair(X1,X3) != X2 ),
inference(er,[status(thm)],[53,theory(equality)]) ).
cnf(67,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[40,theory(equality)]) ).
cnf(108,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,unordered_pair(esk3_0,esk4_0)) ),
inference(spm,[status(thm)],[67,57,theory(equality)]) ).
cnf(119,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[61,theory(equality)]) ).
cnf(137,negated_conjecture,
in(esk3_0,esk5_0),
inference(spm,[status(thm)],[108,119,theory(equality)]) ).
cnf(143,negated_conjecture,
$false,
inference(sr,[status(thm)],[137,28,theory(equality)]) ).
cnf(144,negated_conjecture,
$false,
143,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET920+1.p
% --creating new selector for []
% -running prover on /tmp/tmp7s5L5w/sel_SET920+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET920+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET920+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET920+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
%
%------------------------------------------------------------------------------