TSTP Solution File: SET890+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET890+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 03:44:08 EST 2010
% Result : Theorem 6.16s
% Output : CNFRefutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 254 ( 82 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 322 ( 122 ~; 135 |; 58 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 138 ( 0 sgn 74 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/tmp/tmpyXY89u/sel_SET890+1.p_1',d4_tarski) ).
fof(2,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/tmp/tmpyXY89u/sel_SET890+1.p_1',d10_xboole_0) ).
fof(5,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpyXY89u/sel_SET890+1.p_1',d1_tarski) ).
fof(8,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpyXY89u/sel_SET890+1.p_1',d3_tarski) ).
fof(9,conjecture,
! [X1] : union(singleton(X1)) = X1,
file('/tmp/tmpyXY89u/sel_SET890+1.p_1',t31_zfmisc_1) ).
fof(11,negated_conjecture,
~ ! [X1] : union(singleton(X1)) = X1,
inference(assume_negation,[status(cth)],[9]) ).
fof(14,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(15,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)],[14]) ).
fof(16,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)],[15]) ).
fof(17,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)],[16]) ).
fof(18,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)],[17]) ).
cnf(19,plain,
( in(esk1_3(X2,X1,X3),X2)
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,plain,
( in(X3,esk1_3(X2,X1,X3))
| X1 != union(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(21,plain,
( in(X3,X1)
| X1 != union(X2)
| ~ in(X4,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(25,plain,
! [X1,X2] :
( ( X1 != X2
| ( subset(X1,X2)
& subset(X2,X1) ) )
& ( ~ subset(X1,X2)
| ~ subset(X2,X1)
| X1 = X2 ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(26,plain,
! [X3,X4] :
( ( X3 != X4
| ( subset(X3,X4)
& subset(X4,X3) ) )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X3,X4] :
( ( subset(X3,X4)
| X3 != X4 )
& ( subset(X4,X3)
| X3 != X4 )
& ( ~ subset(X3,X4)
| ~ subset(X4,X3)
| X3 = X4 ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(28,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(37,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)],[5]) ).
fof(38,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)],[37]) ).
fof(39,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)],[38]) ).
fof(40,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)],[39]) ).
fof(41,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)],[40]) ).
cnf(44,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[41]) ).
cnf(45,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[41]) ).
fof(52,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)],[8]) ).
fof(53,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)],[52]) ).
fof(54,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)],[53]) ).
fof(55,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)],[54]) ).
fof(56,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)],[55]) ).
cnf(57,plain,
( subset(X1,X2)
| ~ in(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[56]) ).
cnf(58,plain,
( subset(X1,X2)
| in(esk7_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[56]) ).
fof(60,negated_conjecture,
? [X1] : union(singleton(X1)) != X1,
inference(fof_nnf,[status(thm)],[11]) ).
fof(61,negated_conjecture,
? [X2] : union(singleton(X2)) != X2,
inference(variable_rename,[status(thm)],[60]) ).
fof(62,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(skolemize,[status(esa)],[61]) ).
cnf(63,negated_conjecture,
union(singleton(esk8_0)) != esk8_0,
inference(split_conjunct,[status(thm)],[62]) ).
cnf(70,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[44,theory(equality)]) ).
cnf(93,plain,
( X1 = esk1_3(X2,X3,X4)
| singleton(X1) != X2
| union(X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[45,19,theory(equality)]) ).
cnf(101,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[70,theory(equality)]) ).
cnf(104,plain,
( in(X1,X2)
| union(singleton(X3)) != X2
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[21,101,theory(equality)]) ).
cnf(285,plain,
( in(X1,union(singleton(X2)))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[104,theory(equality)]) ).
cnf(324,plain,
( subset(X1,union(singleton(X2)))
| ~ in(esk7_2(X1,union(singleton(X2))),X2) ),
inference(spm,[status(thm)],[57,285,theory(equality)]) ).
cnf(501,plain,
( X1 = esk1_3(singleton(X1),X2,X3)
| union(singleton(X1)) != X2
| ~ in(X3,X2) ),
inference(er,[status(thm)],[93,theory(equality)]) ).
cnf(1169,plain,
subset(X1,union(singleton(X1))),
inference(spm,[status(thm)],[324,58,theory(equality)]) ).
cnf(1184,plain,
( union(singleton(X1)) = X1
| ~ subset(union(singleton(X1)),X1) ),
inference(spm,[status(thm)],[28,1169,theory(equality)]) ).
cnf(77330,plain,
( in(X1,X2)
| union(singleton(X2)) != X3
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[20,501,theory(equality)]) ).
cnf(79510,plain,
( in(X1,X2)
| ~ in(X1,union(singleton(X2))) ),
inference(er,[status(thm)],[77330,theory(equality)]) ).
cnf(79949,plain,
( in(esk7_2(union(singleton(X1)),X2),X1)
| subset(union(singleton(X1)),X2) ),
inference(spm,[status(thm)],[79510,58,theory(equality)]) ).
cnf(82896,plain,
subset(union(singleton(X1)),X1),
inference(spm,[status(thm)],[57,79949,theory(equality)]) ).
cnf(82948,plain,
( union(singleton(X1)) = X1
| $false ),
inference(rw,[status(thm)],[1184,82896,theory(equality)]) ).
cnf(82949,plain,
union(singleton(X1)) = X1,
inference(cn,[status(thm)],[82948,theory(equality)]) ).
cnf(84660,negated_conjecture,
$false,
inference(rw,[status(thm)],[63,82949,theory(equality)]) ).
cnf(84661,negated_conjecture,
$false,
inference(cn,[status(thm)],[84660,theory(equality)]) ).
cnf(84662,negated_conjecture,
$false,
84661,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET890+1.p
% --creating new selector for []
% -running prover on /tmp/tmpyXY89u/sel_SET890+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET890+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET890+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET890+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
%
%------------------------------------------------------------------------------