TSTP Solution File: SET872+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET872+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.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 03:42:17 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 203 ( 102 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 255 ( 93 ~; 106 |; 50 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 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 : 105 ( 4 sgn 68 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2] : subset(singleton(X1),unordered_pair(X1,X2)),
file('/tmp/tmpq4Fydv/sel_SET872+1.p_1',t12_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmpq4Fydv/sel_SET872+1.p_1',commutativity_k2_tarski) ).
fof(4,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpq4Fydv/sel_SET872+1.p_1',d1_tarski) ).
fof(7,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpq4Fydv/sel_SET872+1.p_1',d3_tarski) ).
fof(8,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpq4Fydv/sel_SET872+1.p_1',d2_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(assume_negation,[status(cth)],[2]) ).
fof(16,negated_conjecture,
? [X1,X2] : ~ subset(singleton(X1),unordered_pair(X1,X2)),
inference(fof_nnf,[status(thm)],[10]) ).
fof(17,negated_conjecture,
? [X3,X4] : ~ subset(singleton(X3),unordered_pair(X3,X4)),
inference(variable_rename,[status(thm)],[16]) ).
fof(18,negated_conjecture,
~ subset(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),
inference(skolemize,[status(esa)],[17]) ).
cnf(19,negated_conjecture,
~ subset(singleton(esk2_0),unordered_pair(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(23,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[23]) ).
fof(25,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4 )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[24]) ).
fof(26,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk4_2(X4,X5),X5)
| esk4_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[25]) ).
cnf(30,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[26]) ).
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)],[7]) ).
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(esk6_2(X4,X5),X4)
& ~ in(esk6_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(esk6_2(X4,X5),X4)
& ~ in(esk6_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(esk6_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk6_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[40]) ).
cnf(42,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(43,plain,
( subset(X1,X2)
| in(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(45,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)],[8]) ).
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) ) ) )
& ( ? [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)],[45]) ).
fof(47,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)],[46]) ).
fof(48,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)],[47]) ).
fof(49,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)],[48]) ).
cnf(53,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(59,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[53,theory(equality)]) ).
cnf(60,plain,
( X1 = esk6_2(X2,X3)
| subset(X2,X3)
| singleton(X1) != X2 ),
inference(spm,[status(thm)],[30,43,theory(equality)]) ).
cnf(80,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[59,theory(equality)]) ).
cnf(83,plain,
in(X1,unordered_pair(X1,X2)),
inference(spm,[status(thm)],[80,21,theory(equality)]) ).
cnf(101,plain,
( X1 = esk6_2(singleton(X1),X2)
| subset(singleton(X1),X2) ),
inference(er,[status(thm)],[60,theory(equality)]) ).
cnf(103,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[42,101,theory(equality)]) ).
cnf(106,negated_conjecture,
~ in(esk2_0,unordered_pair(esk2_0,esk3_0)),
inference(spm,[status(thm)],[19,103,theory(equality)]) ).
cnf(108,negated_conjecture,
$false,
inference(rw,[status(thm)],[106,83,theory(equality)]) ).
cnf(109,negated_conjecture,
$false,
inference(cn,[status(thm)],[108,theory(equality)]) ).
cnf(110,negated_conjecture,
$false,
109,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET872+1.p
% --creating new selector for []
% -running prover on /tmp/tmpq4Fydv/sel_SET872+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET872+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET872+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET872+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
%
%------------------------------------------------------------------------------