%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET960+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 03:54:48 EST 2010
% Result : Theorem 0.39s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 18 unt; 0 def)
% Number of atoms : 259 ( 120 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 331 ( 143 ~; 129 |; 49 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 157 ( 27 sgn 68 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/tmp/tmpsNIDQY/sel_SET960+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/tmpsNIDQY/sel_SET960+1.p_1',d2_zfmisc_1) ).
fof(4,conjecture,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/tmp/tmpsNIDQY/sel_SET960+1.p_1',t113_zfmisc_1) ).
fof(9,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpsNIDQY/sel_SET960+1.p_1',d1_xboole_0) ).
fof(11,negated_conjecture,
~ ! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(15,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).
fof(16,plain,
! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(variable_rename,[status(thm)],[1]) ).
cnf(17,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,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(19,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)],[18]) ).
fof(20,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)],[19]) ).
fof(21,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)],[20]) ).
fof(22,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)],[21]) ).
cnf(24,plain,
( in(esk2_4(X2,X3,X1,X4),X3)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(25,plain,
( in(esk1_4(X2,X3,X1,X4),X2)
| X1 != cartesian_product2(X2,X3)
| ~ in(X4,X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
cnf(26,plain,
( in(X4,X1)
| X1 != cartesian_product2(X2,X3)
| X4 != ordered_pair(X5,X6)
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(34,negated_conjecture,
? [X1,X2] :
( ( cartesian_product2(X1,X2) != empty_set
| ( X1 != empty_set
& X2 != empty_set ) )
& ( cartesian_product2(X1,X2) = empty_set
| X1 = empty_set
| X2 = empty_set ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(35,negated_conjecture,
? [X3,X4] :
( ( cartesian_product2(X3,X4) != empty_set
| ( X3 != empty_set
& X4 != empty_set ) )
& ( cartesian_product2(X3,X4) = empty_set
| X3 = empty_set
| X4 = empty_set ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,negated_conjecture,
( ( cartesian_product2(esk7_0,esk8_0) != empty_set
| ( esk7_0 != empty_set
& esk8_0 != empty_set ) )
& ( cartesian_product2(esk7_0,esk8_0) = empty_set
| esk7_0 = empty_set
| esk8_0 = empty_set ) ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,negated_conjecture,
( ( esk7_0 != empty_set
| cartesian_product2(esk7_0,esk8_0) != empty_set )
& ( esk8_0 != empty_set
| cartesian_product2(esk7_0,esk8_0) != empty_set )
& ( cartesian_product2(esk7_0,esk8_0) = empty_set
| esk7_0 = empty_set
| esk8_0 = empty_set ) ),
inference(distribute,[status(thm)],[36]) ).
cnf(38,negated_conjecture,
( esk8_0 = empty_set
| esk7_0 = empty_set
| cartesian_product2(esk7_0,esk8_0) = empty_set ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,negated_conjecture,
( cartesian_product2(esk7_0,esk8_0) != empty_set
| esk8_0 != empty_set ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,negated_conjecture,
( cartesian_product2(esk7_0,esk8_0) != empty_set
| esk7_0 != empty_set ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(51,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(52,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk10_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[52]) ).
fof(54,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk10_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[53]) ).
cnf(55,plain,
( X1 = empty_set
| in(esk10_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(56,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[54]) ).
cnf(60,plain,
( in(X4,X1)
| unordered_pair(unordered_pair(X5,X6),singleton(X5)) != X4
| cartesian_product2(X2,X3) != X1
| ~ in(X6,X3)
| ~ in(X5,X2) ),
inference(rw,[status(thm)],[26,17,theory(equality)]),
[unfolding] ).
cnf(71,plain,
( empty_set != X1
| cartesian_product2(X1,X2) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[56,25,theory(equality)]) ).
cnf(73,plain,
( empty_set != X1
| cartesian_product2(X2,X1) != X3
| ~ in(X4,X3) ),
inference(spm,[status(thm)],[56,24,theory(equality)]) ).
cnf(83,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| cartesian_product2(X4,X5) != X3
| ~ in(X2,X5)
| ~ in(X1,X4) ),
inference(er,[status(thm)],[60,theory(equality)]) ).
cnf(96,plain,
( empty_set != X1
| ~ in(X2,cartesian_product2(X1,X3)) ),
inference(er,[status(thm)],[71,theory(equality)]) ).
cnf(99,plain,
( empty_set = cartesian_product2(X1,X2)
| empty_set != X1 ),
inference(spm,[status(thm)],[96,55,theory(equality)]) ).
cnf(106,negated_conjecture,
esk7_0 != empty_set,
inference(spm,[status(thm)],[40,99,theory(equality)]) ).
cnf(109,plain,
( empty_set != X1
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[96,99,theory(equality)]) ).
cnf(115,negated_conjecture,
( cartesian_product2(esk7_0,esk8_0) = empty_set
| esk8_0 = empty_set ),
inference(sr,[status(thm)],[38,106,theory(equality)]) ).
fof(120,plain,
( ~ epred1_0
<=> ! [X1] : empty_set != X1 ),
introduced(definition),
[split] ).
cnf(121,plain,
( epred1_0
| empty_set != X1 ),
inference(split_equiv,[status(thm)],[120]) ).
fof(122,plain,
( ~ epred2_0
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(definition),
[split] ).
cnf(123,plain,
( epred2_0
| ~ in(X2,empty_set) ),
inference(split_equiv,[status(thm)],[122]) ).
cnf(124,plain,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[109,120,theory(equality)]),122,theory(equality)]),
[split] ).
cnf(125,plain,
epred1_0,
inference(er,[status(thm)],[121,theory(equality)]) ).
cnf(127,plain,
( ~ epred2_0
| $false ),
inference(rw,[status(thm)],[124,125,theory(equality)]) ).
cnf(128,plain,
~ epred2_0,
inference(cn,[status(thm)],[127,theory(equality)]) ).
cnf(135,plain,
~ in(X2,empty_set),
inference(sr,[status(thm)],[123,128,theory(equality)]) ).
cnf(137,plain,
( cartesian_product2(empty_set,X1) != X2
| ~ in(X3,X2) ),
inference(spm,[status(thm)],[135,25,theory(equality)]) ).
cnf(183,plain,
~ in(X1,cartesian_product2(empty_set,X2)),
inference(er,[status(thm)],[137,theory(equality)]) ).
cnf(187,plain,
empty_set = cartesian_product2(empty_set,X1),
inference(spm,[status(thm)],[183,55,theory(equality)]) ).
cnf(202,plain,
~ in(X1,empty_set),
inference(rw,[status(thm)],[183,187,theory(equality)]) ).
cnf(222,plain,
( empty_set != X1
| ~ in(X2,cartesian_product2(X3,X1)) ),
inference(er,[status(thm)],[73,theory(equality)]) ).
cnf(229,plain,
( empty_set = cartesian_product2(X2,X1)
| empty_set != X1 ),
inference(spm,[status(thm)],[222,55,theory(equality)]) ).
cnf(243,negated_conjecture,
esk8_0 != empty_set,
inference(spm,[status(thm)],[39,229,theory(equality)]) ).
cnf(250,negated_conjecture,
cartesian_product2(esk7_0,esk8_0) = empty_set,
inference(sr,[status(thm)],[115,243,theory(equality)]) ).
cnf(522,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[83,theory(equality)]) ).
cnf(3793,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),empty_set)
| ~ in(X2,esk8_0)
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[522,250,theory(equality)]) ).
cnf(3839,negated_conjecture,
( ~ in(X2,esk8_0)
| ~ in(X1,esk7_0) ),
inference(sr,[status(thm)],[3793,202,theory(equality)]) ).
fof(3884,plain,
( ~ epred3_0
<=> ! [X2] : ~ in(X2,esk8_0) ),
introduced(definition),
[split] ).
cnf(3885,plain,
( epred3_0
| ~ in(X2,esk8_0) ),
inference(split_equiv,[status(thm)],[3884]) ).
fof(3886,plain,
( ~ epred4_0
<=> ! [X1] : ~ in(X1,esk7_0) ),
introduced(definition),
[split] ).
cnf(3887,plain,
( epred4_0
| ~ in(X1,esk7_0) ),
inference(split_equiv,[status(thm)],[3886]) ).
cnf(3888,negated_conjecture,
( ~ epred4_0
| ~ epred3_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[3839,3884,theory(equality)]),3886,theory(equality)]),
[split] ).
cnf(3899,negated_conjecture,
( epred3_0
| empty_set = esk8_0 ),
inference(spm,[status(thm)],[3885,55,theory(equality)]) ).
cnf(3920,negated_conjecture,
epred3_0,
inference(sr,[status(thm)],[3899,243,theory(equality)]) ).
cnf(3924,negated_conjecture,
( ~ epred4_0
| $false ),
inference(rw,[status(thm)],[3888,3920,theory(equality)]) ).
cnf(3925,negated_conjecture,
~ epred4_0,
inference(cn,[status(thm)],[3924,theory(equality)]) ).
cnf(3930,negated_conjecture,
~ in(X1,esk7_0),
inference(sr,[status(thm)],[3887,3925,theory(equality)]) ).
cnf(3931,negated_conjecture,
empty_set = esk7_0,
inference(spm,[status(thm)],[3930,55,theory(equality)]) ).
cnf(3952,negated_conjecture,
$false,
inference(sr,[status(thm)],[3931,106,theory(equality)]) ).
cnf(3953,negated_conjecture,
$false,
3952,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET960+1.p
% --creating new selector for []
% -running prover on /tmp/tmpsNIDQY/sel_SET960+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET960+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET960+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET960+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
%
%------------------------------------------------------------------------------