TSTP Solution File: SET909+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET909+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 03:46:22 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 236 ( 120 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 292 ( 107 ~; 125 |; 54 &)
% ( 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 129 ( 10 sgn 74 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,conjecture,
! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
file('/tmp/tmp0Q2ZkF/sel_SET909+1.p_1',t50_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/tmp0Q2ZkF/sel_SET909+1.p_1',d2_xboole_0) ).
fof(5,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/tmp/tmp0Q2ZkF/sel_SET909+1.p_1',commutativity_k2_xboole_0) ).
fof(7,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp0Q2ZkF/sel_SET909+1.p_1',commutativity_k2_tarski) ).
fof(11,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmp0Q2ZkF/sel_SET909+1.p_1',d1_xboole_0) ).
fof(12,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmp0Q2ZkF/sel_SET909+1.p_1',d2_tarski) ).
fof(14,negated_conjecture,
~ ! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
inference(assume_negation,[status(cth)],[1]) ).
fof(19,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(20,negated_conjecture,
? [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) = empty_set,
inference(fof_nnf,[status(thm)],[14]) ).
fof(21,negated_conjecture,
? [X4,X5,X6] : set_union2(unordered_pair(X4,X5),X6) = empty_set,
inference(variable_rename,[status(thm)],[20]) ).
fof(22,negated_conjecture,
set_union2(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set,
inference(skolemize,[status(esa)],[21]) ).
cnf(23,negated_conjecture,
set_union2(unordered_pair(esk1_0,esk2_0),esk3_0) = empty_set,
inference(split_conjunct,[status(thm)],[22]) ).
fof(27,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(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) ) ) )
& ( ? [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)],[27]) ).
fof(29,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(esk5_3(X5,X6,X7),X7)
| ( ~ in(esk5_3(X5,X6,X7),X5)
& ~ in(esk5_3(X5,X6,X7),X6) ) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| in(esk5_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(skolemize,[status(esa)],[28]) ).
fof(30,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(esk5_3(X5,X6,X7),X7)
| ( ~ in(esk5_3(X5,X6,X7),X5)
& ~ in(esk5_3(X5,X6,X7),X6) ) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| in(esk5_3(X5,X6,X7),X6) ) )
| X7 = set_union2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[29]) ).
fof(31,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(esk5_3(X5,X6,X7),X5)
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( ~ in(esk5_3(X5,X6,X7),X6)
| ~ in(esk5_3(X5,X6,X7),X7)
| X7 = set_union2(X5,X6) )
& ( in(esk5_3(X5,X6,X7),X7)
| in(esk5_3(X5,X6,X7),X5)
| in(esk5_3(X5,X6,X7),X6)
| X7 = set_union2(X5,X6) ) ),
inference(distribute,[status(thm)],[30]) ).
cnf(35,plain,
( in(X4,X1)
| X1 != set_union2(X2,X3)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(41,plain,
! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
inference(variable_rename,[status(thm)],[5]) ).
cnf(42,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[41]) ).
fof(46,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(47,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[46]) ).
fof(56,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(57,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[56]) ).
fof(58,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[57]) ).
fof(59,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[58]) ).
cnf(61,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(62,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)],[12]) ).
fof(63,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)],[62]) ).
fof(64,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)],[63]) ).
fof(65,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)],[64]) ).
fof(66,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)],[65]) ).
cnf(67,plain,
( X1 = unordered_pair(X2,X3)
| esk8_3(X2,X3,X1) = X3
| esk8_3(X2,X3,X1) = X2
| in(esk8_3(X2,X3,X1),X1) ),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(68,plain,
( X1 = unordered_pair(X2,X3)
| ~ in(esk8_3(X2,X3,X1),X1)
| esk8_3(X2,X3,X1) != X3 ),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(70,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[66]) ).
cnf(76,negated_conjecture,
set_union2(esk3_0,unordered_pair(esk1_0,esk2_0)) = empty_set,
inference(rw,[status(thm)],[23,42,theory(equality)]) ).
cnf(80,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[70,theory(equality)]) ).
cnf(92,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[35,theory(equality)]) ).
cnf(107,plain,
( esk8_3(X2,X3,X1) = X2
| esk8_3(X2,X3,X1) = X3
| unordered_pair(X2,X3) = X1
| empty_set != X1 ),
inference(spm,[status(thm)],[61,67,theory(equality)]) ).
cnf(136,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[80,theory(equality)]) ).
cnf(139,plain,
( esk8_3(X1,X2,empty_set) = X2
| esk8_3(X1,X2,empty_set) = X1
| unordered_pair(X1,X2) = empty_set ),
inference(er,[status(thm)],[107,theory(equality)]) ).
cnf(140,plain,
( esk8_3(X3,X4,empty_set) = X4
| unordered_pair(X3,X4) = empty_set
| X3 != X4 ),
inference(ef,[status(thm)],[139,theory(equality)]) ).
cnf(146,plain,
( esk8_3(X1,X1,empty_set) = X1
| unordered_pair(X1,X1) = empty_set ),
inference(er,[status(thm)],[140,theory(equality)]) ).
cnf(150,plain,
( unordered_pair(X1,X1) = empty_set
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[68,146,theory(equality)]) ).
cnf(154,plain,
empty_set != unordered_pair(X1,X2),
inference(spm,[status(thm)],[61,136,theory(equality)]) ).
cnf(157,plain,
( empty_set = unordered_pair(X1,X1)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[47,150,theory(equality)]) ).
cnf(182,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[157,154,theory(equality)]) ).
cnf(251,negated_conjecture,
( in(X1,empty_set)
| ~ in(X1,unordered_pair(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[92,76,theory(equality)]) ).
cnf(262,negated_conjecture,
~ in(X1,unordered_pair(esk1_0,esk2_0)),
inference(sr,[status(thm)],[251,182,theory(equality)]) ).
cnf(263,negated_conjecture,
$false,
inference(spm,[status(thm)],[262,136,theory(equality)]) ).
cnf(270,negated_conjecture,
$false,
263,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET909+1.p
% --creating new selector for []
% -running prover on /tmp/tmp0Q2ZkF/sel_SET909+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET909+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET909+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET909+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
%
%------------------------------------------------------------------------------