TSTP Solution File: SET908+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET908+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 03:46:18 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 20 unt; 0 def)
% Number of atoms : 226 ( 97 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 270 ( 101 ~; 119 |; 44 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 122 ( 8 sgn 66 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
file('/tmp/tmp0xH4f_/sel_SET908+1.p_1',t49_zfmisc_1) ).
fof(3,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/tmp/tmp0xH4f_/sel_SET908+1.p_1',d2_xboole_0) ).
fof(5,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmp0xH4f_/sel_SET908+1.p_1',commutativity_k2_xboole_0) ).
fof(7,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmp0xH4f_/sel_SET908+1.p_1',d1_tarski) ).
fof(8,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/tmp/tmp0xH4f_/sel_SET908+1.p_1',idempotence_k2_xboole_0) ).
fof(11,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmp0xH4f_/sel_SET908+1.p_1',d1_xboole_0) ).
fof(13,negated_conjecture,
~ ! [X1,X2] : set_union2(singleton(X1),X2) != empty_set,
inference(assume_negation,[status(cth)],[1]) ).
fof(18,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(19,negated_conjecture,
? [X1,X2] : set_union2(singleton(X1),X2) = empty_set,
inference(fof_nnf,[status(thm)],[13]) ).
fof(20,negated_conjecture,
? [X3,X4] : set_union2(singleton(X3),X4) = empty_set,
inference(variable_rename,[status(thm)],[19]) ).
fof(21,negated_conjecture,
set_union2(singleton(esk1_0),esk2_0) = empty_set,
inference(skolemize,[status(esa)],[20]) ).
cnf(22,negated_conjecture,
set_union2(singleton(esk1_0),esk2_0) = empty_set,
inference(split_conjunct,[status(thm)],[21]) ).
fof(26,plain,
! [X1,X2,X3] :
( ( X3 != set_union2(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_union2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(27,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(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_union2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X5,X6,X7] :
( ( X7 != set_union2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6) )
& ( ( ~ in(X8,X5)
& ~ in(X8,X6) )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk4_3(X5,X6,X7),X7)
| ( ~ in(esk4_3(X5,X6,X7),X5)
& ~ in(esk4_3(X5,X6,X7),X6) ) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[27]) ).
fof(29,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_union2(X5,X6) )
& ( ( ( ~ in(esk4_3(X5,X6,X7),X7)
| ( ~ in(esk4_3(X5,X6,X7),X5)
& ~ in(esk4_3(X5,X6,X7),X6) ) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[28]) ).
fof(30,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(X8,X5)
| in(X8,X6)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(X8,X6)
| in(X8,X7)
| X7 != set_union2(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X5)
| ~ in(esk4_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk4_3(X5,X6,X7),X6)
| ~ in(esk4_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk4_3(X5,X6,X7),X7)
| in(esk4_3(X5,X6,X7),X5)
| in(esk4_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[29]) ).
cnf(31,plain,
( X1 = set_union2(X2,X3)
| in(esk4_3(X2,X3,X1),X3)
| in(esk4_3(X2,X3,X1),X2)
| in(esk4_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(32,plain,
( X1 = set_union2(X2,X3)
| ~ in(esk4_3(X2,X3,X1),X1)
| ~ in(esk4_3(X2,X3,X1),X3) ),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(34,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(40,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(41,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[40]) ).
fof(45,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)],[7]) ).
fof(46,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)],[45]) ).
fof(47,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)],[46]) ).
fof(48,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)],[47]) ).
fof(49,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)],[48]) ).
cnf(52,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[49]) ).
cnf(53,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(54,plain,
! [X3,X4] : set_union2(X3,X3) = X3,
inference(variable_rename,[status(thm)],[8]) ).
cnf(55,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[54]) ).
fof(62,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(63,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[62]) ).
fof(64,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[64]) ).
cnf(67,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(71,negated_conjecture,
set_union2(esk2_0,singleton(esk1_0)) = empty_set,
inference(rw,[status(thm)],[22,41,theory(equality)]) ).
cnf(74,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[52,theory(equality)]) ).
cnf(84,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[34,theory(equality)]) ).
cnf(109,plain,
( set_union2(X2,X3) = X1
| in(esk4_3(X2,X3,X1),X2)
| in(esk4_3(X2,X3,X1),X3)
| empty_set != X1 ),
inference(spm,[status(thm)],[67,31,theory(equality)]) ).
cnf(132,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[74,theory(equality)]) ).
cnf(134,plain,
( set_union2(X1,X2) = empty_set
| in(esk4_3(X1,X2,empty_set),X2)
| in(esk4_3(X1,X2,empty_set),X1) ),
inference(er,[status(thm)],[109,theory(equality)]) ).
cnf(135,plain,
empty_set != singleton(X1),
inference(spm,[status(thm)],[67,132,theory(equality)]) ).
cnf(140,plain,
( set_union2(X3,X3) = empty_set
| in(esk4_3(X3,X3,empty_set),X3) ),
inference(ef,[status(thm)],[134,theory(equality)]) ).
cnf(150,plain,
( X3 = empty_set
| in(esk4_3(X3,X3,empty_set),X3) ),
inference(rw,[status(thm)],[140,55,theory(equality)]) ).
cnf(153,plain,
( X1 = esk4_3(X2,X2,empty_set)
| X2 = empty_set
| singleton(X1) != X2 ),
inference(spm,[status(thm)],[53,150,theory(equality)]) ).
cnf(161,plain,
( X1 = esk4_3(singleton(X1),singleton(X1),empty_set)
| singleton(X1) = empty_set ),
inference(er,[status(thm)],[153,theory(equality)]) ).
cnf(162,plain,
esk4_3(singleton(X1),singleton(X1),empty_set) = X1,
inference(sr,[status(thm)],[161,135,theory(equality)]) ).
cnf(168,plain,
( set_union2(singleton(X1),singleton(X1)) = empty_set
| ~ in(X1,singleton(X1))
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[32,162,theory(equality)]) ).
cnf(171,plain,
( singleton(X1) = empty_set
| ~ in(X1,singleton(X1))
| ~ in(X1,empty_set) ),
inference(rw,[status(thm)],[168,55,theory(equality)]) ).
cnf(172,plain,
( singleton(X1) = empty_set
| $false
| ~ in(X1,empty_set) ),
inference(rw,[status(thm)],[171,132,theory(equality)]) ).
cnf(173,plain,
( singleton(X1) = empty_set
| ~ in(X1,empty_set) ),
inference(cn,[status(thm)],[172,theory(equality)]) ).
cnf(174,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[173,135,theory(equality)]) ).
cnf(192,negated_conjecture,
( in(X1,empty_set)
| ~ in(X1,singleton(esk1_0)) ),
inference(spm,[status(thm)],[84,71,theory(equality)]) ).
cnf(202,negated_conjecture,
~ in(X1,singleton(esk1_0)),
inference(sr,[status(thm)],[192,174,theory(equality)]) ).
cnf(203,negated_conjecture,
$false,
inference(spm,[status(thm)],[202,132,theory(equality)]) ).
cnf(212,negated_conjecture,
$false,
203,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET908+1.p
% --creating new selector for []
% -running prover on /tmp/tmp0xH4f_/sel_SET908+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET908+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET908+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET908+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
%
%------------------------------------------------------------------------------