TSTP Solution File: SET884+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET884+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:43:24 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 211 ( 114 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 276 ( 103 ~; 107 |; 60 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 66 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] :
~ ( subset(singleton(X1),unordered_pair(X2,X3))
& X1 != X2
& X1 != X3 ),
file('/tmp/tmpF-5BRC/sel_SET884+1.p_1',t25_zfmisc_1) ).
fof(4,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpF-5BRC/sel_SET884+1.p_1',d1_tarski) ).
fof(7,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpF-5BRC/sel_SET884+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/tmpF-5BRC/sel_SET884+1.p_1',d2_tarski) ).
fof(10,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( subset(singleton(X1),unordered_pair(X2,X3))
& X1 != X2
& X1 != X3 ),
inference(assume_negation,[status(cth)],[1]) ).
fof(13,negated_conjecture,
? [X1,X2,X3] :
( subset(singleton(X1),unordered_pair(X2,X3))
& X1 != X2
& X1 != X3 ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(14,negated_conjecture,
? [X4,X5,X6] :
( subset(singleton(X4),unordered_pair(X5,X6))
& X4 != X5
& X4 != X6 ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,negated_conjecture,
( subset(singleton(esk1_0),unordered_pair(esk2_0,esk3_0))
& esk1_0 != esk2_0
& esk1_0 != esk3_0 ),
inference(skolemize,[status(esa)],[14]) ).
cnf(16,negated_conjecture,
esk1_0 != esk3_0,
inference(split_conjunct,[status(thm)],[15]) ).
cnf(17,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[15]) ).
cnf(18,negated_conjecture,
subset(singleton(esk1_0),unordered_pair(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[15]) ).
fof(24,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(25,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)],[24]) ).
fof(26,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4 )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[25]) ).
fof(27,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4 )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[26]) ).
fof(28,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk5_2(X4,X5),X5)
| esk5_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[27]) ).
cnf(31,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(39,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(40,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)],[39]) ).
fof(41,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[40]) ).
fof(42,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk7_2(X4,X5),X4)
& ~ in(esk7_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[41]) ).
fof(43,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk7_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk7_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[42]) ).
cnf(46,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(47,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(48,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)],[47]) ).
fof(49,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(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[48]) ).
fof(50,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(esk8_3(X5,X6,X7),X7)
| ( esk8_3(X5,X6,X7) != X5
& esk8_3(X5,X6,X7) != X6 ) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[49]) ).
fof(51,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) )
& ( esk8_3(X5,X6,X7) != X5
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk8_3(X5,X6,X7) != X6
| ~ in(esk8_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| esk8_3(X5,X6,X7) = X5
| esk8_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[50]) ).
cnf(57,plain,
( X4 = X3
| X4 = X2
| X1 != unordered_pair(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[51]) ).
cnf(60,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[31,theory(equality)]) ).
cnf(68,negated_conjecture,
( in(X1,unordered_pair(esk2_0,esk3_0))
| ~ in(X1,singleton(esk1_0)) ),
inference(spm,[status(thm)],[46,18,theory(equality)]) ).
cnf(69,plain,
( X1 = X2
| X3 = X2
| ~ in(X2,unordered_pair(X1,X3)) ),
inference(er,[status(thm)],[57,theory(equality)]) ).
cnf(79,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[60,theory(equality)]) ).
cnf(89,negated_conjecture,
in(esk1_0,unordered_pair(esk2_0,esk3_0)),
inference(spm,[status(thm)],[68,79,theory(equality)]) ).
cnf(121,negated_conjecture,
( esk3_0 = esk1_0
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[69,89,theory(equality)]) ).
cnf(127,negated_conjecture,
esk2_0 = esk1_0,
inference(sr,[status(thm)],[121,16,theory(equality)]) ).
cnf(128,negated_conjecture,
$false,
inference(sr,[status(thm)],[127,17,theory(equality)]) ).
cnf(129,negated_conjecture,
$false,
128,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET884+1.p
% --creating new selector for []
% -running prover on /tmp/tmpF-5BRC/sel_SET884+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET884+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET884+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET884+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
%
%------------------------------------------------------------------------------