TSTP Solution File: SET921+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET921+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 03:47:34 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 45 ( 5 unt; 0 def)
% Number of atoms : 229 ( 80 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 291 ( 107 ~; 124 |; 52 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 93 ( 4 sgn 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/tmp/tmpLqcsHv/sel_SET921+1.p_1',d4_xboole_0) ).
fof(3,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpLqcsHv/sel_SET921+1.p_1',d1_tarski) ).
fof(4,conjecture,
! [X1,X2,X3] :
( in(X1,set_difference(X2,singleton(X3)))
<=> ( in(X1,X2)
& X1 != X3 ) ),
file('/tmp/tmpLqcsHv/sel_SET921+1.p_1',t64_zfmisc_1) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3] :
( in(X1,set_difference(X2,singleton(X3)))
<=> ( in(X1,X2)
& X1 != X3 ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(9,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).
fof(14,plain,
! [X1,X2,X3] :
( ( X3 != set_difference(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_difference(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(15,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(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_difference(X5,X6) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
| ~ in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) )
& ( in(esk2_3(X5,X6,X7),X7)
| ( in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,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_difference(X5,X6) )
& ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
| ~ in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6) )
& ( in(esk2_3(X5,X6,X7),X7)
| ( in(esk2_3(X5,X6,X7),X5)
& ~ in(esk2_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[16]) ).
fof(18,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X7)
| ~ in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X6)
| X7 = set_difference(X5,X6) )
& ( in(esk2_3(X5,X6,X7),X5)
| in(esk2_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) )
& ( ~ in(esk2_3(X5,X6,X7),X6)
| in(esk2_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) ) ),
inference(distribute,[status(thm)],[17]) ).
cnf(22,plain,
( in(X4,X1)
| in(X4,X3)
| X1 != set_difference(X2,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(23,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(24,plain,
( in(X4,X2)
| X1 != set_difference(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(25,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)],[3]) ).
fof(26,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)],[25]) ).
fof(27,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[26]) ).
fof(28,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[27]) ).
fof(29,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[28]) ).
cnf(32,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[29]) ).
cnf(33,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[29]) ).
fof(34,negated_conjecture,
? [X1,X2,X3] :
( ( ~ in(X1,set_difference(X2,singleton(X3)))
| ~ in(X1,X2)
| X1 = X3 )
& ( in(X1,set_difference(X2,singleton(X3)))
| ( in(X1,X2)
& X1 != X3 ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(35,negated_conjecture,
? [X4,X5,X6] :
( ( ~ in(X4,set_difference(X5,singleton(X6)))
| ~ in(X4,X5)
| X4 = X6 )
& ( in(X4,set_difference(X5,singleton(X6)))
| ( in(X4,X5)
& X4 != X6 ) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( ( ~ in(esk4_0,set_difference(esk5_0,singleton(esk6_0)))
| ~ in(esk4_0,esk5_0)
| esk4_0 = esk6_0 )
& ( in(esk4_0,set_difference(esk5_0,singleton(esk6_0)))
| ( in(esk4_0,esk5_0)
& esk4_0 != esk6_0 ) ) ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,negated_conjecture,
( ( ~ in(esk4_0,set_difference(esk5_0,singleton(esk6_0)))
| ~ in(esk4_0,esk5_0)
| esk4_0 = esk6_0 )
& ( in(esk4_0,esk5_0)
| in(esk4_0,set_difference(esk5_0,singleton(esk6_0))) )
& ( esk4_0 != esk6_0
| in(esk4_0,set_difference(esk5_0,singleton(esk6_0))) ) ),
inference(distribute,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
( in(esk4_0,set_difference(esk5_0,singleton(esk6_0)))
| esk4_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,negated_conjecture,
( in(esk4_0,set_difference(esk5_0,singleton(esk6_0)))
| in(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,negated_conjecture,
( esk4_0 = esk6_0
| ~ in(esk4_0,esk5_0)
| ~ in(esk4_0,set_difference(esk5_0,singleton(esk6_0))) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(47,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[32,theory(equality)]) ).
cnf(56,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[24,theory(equality)]) ).
cnf(57,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(er,[status(thm)],[23,theory(equality)]) ).
cnf(58,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[22,theory(equality)]) ).
cnf(69,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[47,theory(equality)]) ).
cnf(70,negated_conjecture,
( ~ in(esk4_0,singleton(esk6_0))
| esk6_0 != esk4_0 ),
inference(spm,[status(thm)],[57,38,theory(equality)]) ).
cnf(79,negated_conjecture,
in(esk4_0,esk5_0),
inference(spm,[status(thm)],[56,39,theory(equality)]) ).
cnf(87,negated_conjecture,
( esk6_0 = esk4_0
| ~ in(esk4_0,set_difference(esk5_0,singleton(esk6_0)))
| $false ),
inference(rw,[status(thm)],[40,79,theory(equality)]) ).
cnf(88,negated_conjecture,
( esk6_0 = esk4_0
| ~ in(esk4_0,set_difference(esk5_0,singleton(esk6_0))) ),
inference(cn,[status(thm)],[87,theory(equality)]) ).
cnf(100,negated_conjecture,
( esk6_0 = esk4_0
| in(esk4_0,singleton(esk6_0))
| ~ in(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[88,58,theory(equality)]) ).
cnf(102,negated_conjecture,
( esk6_0 = esk4_0
| in(esk4_0,singleton(esk6_0))
| $false ),
inference(rw,[status(thm)],[100,79,theory(equality)]) ).
cnf(103,negated_conjecture,
( esk6_0 = esk4_0
| in(esk4_0,singleton(esk6_0)) ),
inference(cn,[status(thm)],[102,theory(equality)]) ).
cnf(109,negated_conjecture,
( X1 = esk4_0
| esk6_0 = esk4_0
| singleton(X1) != singleton(esk6_0) ),
inference(spm,[status(thm)],[33,103,theory(equality)]) ).
cnf(111,negated_conjecture,
esk6_0 = esk4_0,
inference(er,[status(thm)],[109,theory(equality)]) ).
cnf(123,negated_conjecture,
( $false
| ~ in(esk4_0,singleton(esk6_0)) ),
inference(rw,[status(thm)],[70,111,theory(equality)]) ).
cnf(124,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[123,111,theory(equality)]),69,theory(equality)]) ).
cnf(125,negated_conjecture,
$false,
inference(cn,[status(thm)],[124,theory(equality)]) ).
cnf(126,negated_conjecture,
$false,
125,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET921+1.p
% --creating new selector for []
% -running prover on /tmp/tmpLqcsHv/sel_SET921+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET921+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET921+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET921+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
%
%------------------------------------------------------------------------------