TSTP Solution File: SET949+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET949+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 03:50:30 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 143 ( 62 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 187 ( 73 ~; 69 |; 43 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 117 ( 8 sgn 70 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmp8gn2Gt/sel_SET949+1.p_1',d5_tarski) ).
fof(2,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/tmp/tmp8gn2Gt/sel_SET949+1.p_1',d2_zfmisc_1) ).
fof(4,conjecture,
! [X1,X2,X3] :
~ ( in(X1,cartesian_product2(X2,X3))
& ! [X4,X5] : ordered_pair(X4,X5) != X1 ),
file('/tmp/tmp8gn2Gt/sel_SET949+1.p_1',t102_zfmisc_1) ).
fof(6,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/tmp/tmp8gn2Gt/sel_SET949+1.p_1',commutativity_k2_tarski) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( in(X1,cartesian_product2(X2,X3))
& ! [X4,X5] : ordered_pair(X4,X5) != X1 ),
inference(assume_negation,[status(cth)],[4]) ).
fof(13,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[13]) ).
fof(15,plain,
! [X1,X2,X3] :
( ( X3 != cartesian_product2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) )
& ( ! [X5,X6] :
( ~ in(X5,X1)
| ~ in(X6,X2)
| X4 != ordered_pair(X5,X6) )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ! [X5,X6] :
( ~ in(X5,X1)
| ~ in(X6,X2)
| X4 != ordered_pair(X5,X6) ) )
& ( in(X4,X3)
| ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) )
| X3 = cartesian_product2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(16,plain,
! [X7,X8,X9] :
( ( X9 != cartesian_product2(X7,X8)
| ! [X10] :
( ( ~ in(X10,X9)
| ? [X11,X12] :
( in(X11,X7)
& in(X12,X8)
& X10 = ordered_pair(X11,X12) ) )
& ( ! [X13,X14] :
( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14) )
| in(X10,X9) ) ) )
& ( ? [X15] :
( ( ~ in(X15,X9)
| ! [X16,X17] :
( ~ in(X16,X7)
| ~ in(X17,X8)
| X15 != ordered_pair(X16,X17) ) )
& ( in(X15,X9)
| ? [X18,X19] :
( in(X18,X7)
& in(X19,X8)
& X15 = ordered_pair(X18,X19) ) ) )
| X9 = cartesian_product2(X7,X8) ) ),
inference(variable_rename,[status(thm)],[15]) ).
fof(17,plain,
! [X7,X8,X9] :
( ( X9 != cartesian_product2(X7,X8)
| ! [X10] :
( ( ~ in(X10,X9)
| ( in(esk1_4(X7,X8,X9,X10),X7)
& in(esk2_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10)) ) )
& ( ! [X13,X14] :
( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14) )
| in(X10,X9) ) ) )
& ( ( ( ~ in(esk3_3(X7,X8,X9),X9)
| ! [X16,X17] :
( ~ in(X16,X7)
| ~ in(X17,X8)
| esk3_3(X7,X8,X9) != ordered_pair(X16,X17) ) )
& ( in(esk3_3(X7,X8,X9),X9)
| ( in(esk4_3(X7,X8,X9),X7)
& in(esk5_3(X7,X8,X9),X8)
& esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9)) ) ) )
| X9 = cartesian_product2(X7,X8) ) ),
inference(skolemize,[status(esa)],[16]) ).
fof(18,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk3_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk3_3(X7,X8,X9),X9) )
& ( in(esk3_3(X7,X8,X9),X9)
| ( in(esk4_3(X7,X8,X9),X7)
& in(esk5_3(X7,X8,X9),X8)
& esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9)) ) ) )
| X9 = cartesian_product2(X7,X8) )
& ( ( ( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14)
| in(X10,X9) )
& ( ~ in(X10,X9)
| ( in(esk1_4(X7,X8,X9,X10),X7)
& in(esk2_4(X7,X8,X9,X10),X8)
& X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10)) ) ) )
| X9 != cartesian_product2(X7,X8) ) ),
inference(shift_quantors,[status(thm)],[17]) ).
fof(19,plain,
! [X7,X8,X9,X10,X13,X14,X16,X17] :
( ( ~ in(X16,X7)
| ~ in(X17,X8)
| esk3_3(X7,X8,X9) != ordered_pair(X16,X17)
| ~ in(esk3_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk4_3(X7,X8,X9),X7)
| in(esk3_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( in(esk5_3(X7,X8,X9),X8)
| in(esk3_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9))
| in(esk3_3(X7,X8,X9),X9)
| X9 = cartesian_product2(X7,X8) )
& ( ~ in(X13,X7)
| ~ in(X14,X8)
| X10 != ordered_pair(X13,X14)
| in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk1_4(X7,X8,X9,X10),X7)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( in(esk2_4(X7,X8,X9,X10),X8)
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) )
& ( X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10))
| ~ in(X10,X9)
| X9 != cartesian_product2(X7,X8) ) ),
inference(distribute,[status(thm)],[18]) ).
cnf(20,plain,
( X4 = ordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4))
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(31,negated_conjecture,
? [X1,X2,X3] :
( in(X1,cartesian_product2(X2,X3))
& ! [X4,X5] : ordered_pair(X4,X5) != X1 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(32,negated_conjecture,
? [X6,X7,X8] :
( in(X6,cartesian_product2(X7,X8))
& ! [X9,X10] : ordered_pair(X9,X10) != X6 ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( in(esk7_0,cartesian_product2(esk8_0,esk9_0))
& ! [X9,X10] : ordered_pair(X9,X10) != esk7_0 ),
inference(skolemize,[status(esa)],[32]) ).
fof(34,negated_conjecture,
! [X9,X10] :
( ordered_pair(X9,X10) != esk7_0
& in(esk7_0,cartesian_product2(esk8_0,esk9_0)) ),
inference(shift_quantors,[status(thm)],[33]) ).
cnf(35,negated_conjecture,
in(esk7_0,cartesian_product2(esk8_0,esk9_0)),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,negated_conjecture,
ordered_pair(X1,X2) != esk7_0,
inference(split_conjunct,[status(thm)],[34]) ).
fof(39,plain,
! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
inference(variable_rename,[status(thm)],[6]) ).
cnf(40,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[39]) ).
cnf(48,plain,
( unordered_pair(unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4)),singleton(esk1_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[20,14,theory(equality)]),
[unfolding] ).
cnf(51,negated_conjecture,
unordered_pair(unordered_pair(X1,X2),singleton(X1)) != esk7_0,
inference(rw,[status(thm)],[36,14,theory(equality)]),
[unfolding] ).
cnf(61,negated_conjecture,
unordered_pair(singleton(X1),unordered_pair(X1,X2)) != esk7_0,
inference(spm,[status(thm)],[51,40,theory(equality)]) ).
cnf(75,plain,
( unordered_pair(singleton(esk1_4(X2,X3,X1,X4)),unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4))) = X4
| cartesian_product2(X2,X3) != X1
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[48,40,theory(equality)]) ).
cnf(95,negated_conjecture,
( X4 != esk7_0
| cartesian_product2(X1,X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[61,75,theory(equality)]) ).
cnf(158,negated_conjecture,
( X1 != esk7_0
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(er,[status(thm)],[95,theory(equality)]) ).
cnf(159,negated_conjecture,
$false,
inference(spm,[status(thm)],[158,35,theory(equality)]) ).
cnf(170,negated_conjecture,
$false,
159,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET949+1.p
% --creating new selector for []
% -running prover on /tmp/tmp8gn2Gt/sel_SET949+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET949+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET949+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET949+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
%
%------------------------------------------------------------------------------