TSTP Solution File: SET082+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET082+1 : TPTP v5.3.0. Bugfixed v5.4.0.
% 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 @ 2800MHz
% Memory : 2005MB
% OS : Linux 2.6.32.26-175.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Fri Jun 15 08:05:30 EDT 2012
% Result : Theorem 0.60s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 145 ( 14 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 161 ( 65 ~; 59 |; 30 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 5 sgn 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] : ~ member(X1,null_class),
file('/tmp/tmpJ3p8hc/sel_SET082+1.p_5',null_class_defn) ).
fof(7,axiom,
! [X1,X3] :
( equal(X1,X3)
<=> ( subclass(X1,X3)
& subclass(X3,X1) ) ),
file('/tmp/tmpJ3p8hc/sel_SET082+1.p_5',extensionality) ).
fof(10,axiom,
! [X1] : equal(singleton(X1),unordered_pair(X1,X1)),
file('/tmp/tmpJ3p8hc/sel_SET082+1.p_5',singleton_set_defn) ).
fof(20,axiom,
! [X1,X3] :
( subclass(X1,X3)
<=> ! [X4] :
( member(X4,X1)
=> member(X4,X3) ) ),
file('/tmp/tmpJ3p8hc/sel_SET082+1.p_5',subclass_defn) ).
fof(24,axiom,
! [X1] : subclass(X1,universal_class),
file('/tmp/tmpJ3p8hc/sel_SET082+1.p_5',class_elements_are_sets) ).
fof(25,axiom,
! [X4,X1,X3] :
( member(X4,unordered_pair(X1,X3))
<=> ( member(X4,universal_class)
& ( equal(X4,X1)
| equal(X4,X3) ) ) ),
file('/tmp/tmpJ3p8hc/sel_SET082+1.p_5',unordered_pair_defn) ).
fof(27,conjecture,
! [X1] :
( ~ member(X1,universal_class)
=> equal(singleton(X1),null_class) ),
file('/tmp/tmpJ3p8hc/sel_SET082+1.p_5',singleton_is_null_class) ).
fof(28,negated_conjecture,
~ ! [X1] :
( ~ member(X1,universal_class)
=> equal(singleton(X1),null_class) ),
inference(assume_negation,[status(cth)],[27]) ).
fof(29,plain,
! [X1] : ~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(30,negated_conjecture,
~ ! [X1] :
( ~ member(X1,universal_class)
=> equal(singleton(X1),null_class) ),
inference(fof_simplification,[status(thm)],[28,theory(equality)]) ).
fof(31,plain,
! [X2] : ~ member(X2,null_class),
inference(variable_rename,[status(thm)],[29]) ).
cnf(32,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[31]) ).
fof(59,plain,
! [X1,X3] :
( ( ~ equal(X1,X3)
| ( subclass(X1,X3)
& subclass(X3,X1) ) )
& ( ~ subclass(X1,X3)
| ~ subclass(X3,X1)
| equal(X1,X3) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(60,plain,
! [X4,X5] :
( ( ~ equal(X4,X5)
| ( subclass(X4,X5)
& subclass(X5,X4) ) )
& ( ~ subclass(X4,X5)
| ~ subclass(X5,X4)
| equal(X4,X5) ) ),
inference(variable_rename,[status(thm)],[59]) ).
fof(61,plain,
! [X4,X5] :
( ( subclass(X4,X5)
| ~ equal(X4,X5) )
& ( subclass(X5,X4)
| ~ equal(X4,X5) )
& ( ~ subclass(X4,X5)
| ~ subclass(X5,X4)
| equal(X4,X5) ) ),
inference(distribute,[status(thm)],[60]) ).
cnf(62,plain,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[61]) ).
fof(73,plain,
! [X2] : equal(singleton(X2),unordered_pair(X2,X2)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(74,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[73]) ).
fof(110,plain,
! [X1,X3] :
( ( ~ subclass(X1,X3)
| ! [X4] :
( ~ member(X4,X1)
| member(X4,X3) ) )
& ( ? [X4] :
( member(X4,X1)
& ~ member(X4,X3) )
| subclass(X1,X3) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(111,plain,
! [X5,X6] :
( ( ~ subclass(X5,X6)
| ! [X7] :
( ~ member(X7,X5)
| member(X7,X6) ) )
& ( ? [X8] :
( member(X8,X5)
& ~ member(X8,X6) )
| subclass(X5,X6) ) ),
inference(variable_rename,[status(thm)],[110]) ).
fof(112,plain,
! [X5,X6] :
( ( ~ subclass(X5,X6)
| ! [X7] :
( ~ member(X7,X5)
| member(X7,X6) ) )
& ( ( member(esk4_2(X5,X6),X5)
& ~ member(esk4_2(X5,X6),X6) )
| subclass(X5,X6) ) ),
inference(skolemize,[status(esa)],[111]) ).
fof(113,plain,
! [X5,X6,X7] :
( ( ~ member(X7,X5)
| member(X7,X6)
| ~ subclass(X5,X6) )
& ( ( member(esk4_2(X5,X6),X5)
& ~ member(esk4_2(X5,X6),X6) )
| subclass(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[112]) ).
fof(114,plain,
! [X5,X6,X7] :
( ( ~ member(X7,X5)
| member(X7,X6)
| ~ subclass(X5,X6) )
& ( member(esk4_2(X5,X6),X5)
| subclass(X5,X6) )
& ( ~ member(esk4_2(X5,X6),X6)
| subclass(X5,X6) ) ),
inference(distribute,[status(thm)],[113]) ).
cnf(116,plain,
( subclass(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[114]) ).
cnf(117,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[114]) ).
fof(128,plain,
! [X2] : subclass(X2,universal_class),
inference(variable_rename,[status(thm)],[24]) ).
cnf(129,plain,
subclass(X1,universal_class),
inference(split_conjunct,[status(thm)],[128]) ).
fof(130,plain,
! [X4,X1,X3] :
( ( ~ member(X4,unordered_pair(X1,X3))
| ( member(X4,universal_class)
& ( equal(X4,X1)
| equal(X4,X3) ) ) )
& ( ~ member(X4,universal_class)
| ( ~ equal(X4,X1)
& ~ equal(X4,X3) )
| member(X4,unordered_pair(X1,X3)) ) ),
inference(fof_nnf,[status(thm)],[25]) ).
fof(131,plain,
! [X5,X6,X7] :
( ( ~ member(X5,unordered_pair(X6,X7))
| ( member(X5,universal_class)
& ( equal(X5,X6)
| equal(X5,X7) ) ) )
& ( ~ member(X5,universal_class)
| ( ~ equal(X5,X6)
& ~ equal(X5,X7) )
| member(X5,unordered_pair(X6,X7)) ) ),
inference(variable_rename,[status(thm)],[130]) ).
fof(132,plain,
! [X5,X6,X7] :
( ( member(X5,universal_class)
| ~ member(X5,unordered_pair(X6,X7)) )
& ( equal(X5,X6)
| equal(X5,X7)
| ~ member(X5,unordered_pair(X6,X7)) )
& ( ~ equal(X5,X6)
| ~ member(X5,universal_class)
| member(X5,unordered_pair(X6,X7)) )
& ( ~ equal(X5,X7)
| ~ member(X5,universal_class)
| member(X5,unordered_pair(X6,X7)) ) ),
inference(distribute,[status(thm)],[131]) ).
cnf(135,plain,
( X1 = X3
| X1 = X2
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[132]) ).
fof(140,negated_conjecture,
? [X1] :
( ~ member(X1,universal_class)
& ~ equal(singleton(X1),null_class) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(141,negated_conjecture,
? [X2] :
( ~ member(X2,universal_class)
& ~ equal(singleton(X2),null_class) ),
inference(variable_rename,[status(thm)],[140]) ).
fof(142,negated_conjecture,
( ~ member(esk5_0,universal_class)
& ~ equal(singleton(esk5_0),null_class) ),
inference(skolemize,[status(esa)],[141]) ).
cnf(143,negated_conjecture,
singleton(esk5_0) != null_class,
inference(split_conjunct,[status(thm)],[142]) ).
cnf(144,negated_conjecture,
~ member(esk5_0,universal_class),
inference(split_conjunct,[status(thm)],[142]) ).
cnf(150,negated_conjecture,
unordered_pair(esk5_0,esk5_0) != null_class,
inference(rw,[status(thm)],[143,74,theory(equality)]),
[unfolding] ).
cnf(184,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[117,129,theory(equality)]) ).
cnf(189,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[32,116,theory(equality)]) ).
cnf(194,plain,
( esk4_2(unordered_pair(X1,X2),X3) = X1
| esk4_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[135,116,theory(equality)]) ).
cnf(259,plain,
( X1 = null_class
| ~ subclass(X1,null_class) ),
inference(spm,[status(thm)],[62,189,theory(equality)]) ).
cnf(273,plain,
( member(esk4_2(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[184,116,theory(equality)]) ).
cnf(605,plain,
( esk4_2(unordered_pair(X4,X5),X6) = X4
| subclass(unordered_pair(X4,X5),X6)
| X5 != X4 ),
inference(ef,[status(thm)],[194,theory(equality)]) ).
cnf(614,plain,
( esk4_2(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[605,theory(equality)]) ).
cnf(901,plain,
( subclass(unordered_pair(X1,X1),X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[273,614,theory(equality)]) ).
cnf(939,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[259,901,theory(equality)]) ).
cnf(941,negated_conjecture,
unordered_pair(esk5_0,esk5_0) = null_class,
inference(spm,[status(thm)],[144,939,theory(equality)]) ).
cnf(1022,negated_conjecture,
$false,
inference(sr,[status(thm)],[941,150,theory(equality)]) ).
cnf(1023,negated_conjecture,
$false,
1022,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET082+1.p
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpJ3p8hc/sel_SET082+1.p_1 with time limit 29
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/tmp/tmpJ3p8hc/sel_SET082+1.p_1']
% -prover status CounterSatisfiable
% -running prover on /tmp/tmpJ3p8hc/sel_SET082+1.p_2 with time limit 89
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=89', '/tmp/tmpJ3p8hc/sel_SET082+1.p_2']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpJ3p8hc/sel_SET082+1.p_3 with time limit 119
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=119', '/tmp/tmpJ3p8hc/sel_SET082+1.p_3']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpJ3p8hc/sel_SET082+1.p_4 with time limit 149
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=149', '/tmp/tmpJ3p8hc/sel_SET082+1.p_4']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpJ3p8hc/sel_SET082+1.p_5 with time limit 299
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=299', '/tmp/tmpJ3p8hc/sel_SET082+1.p_5']
% -prover status Theorem
% Problem SET082+1.p solved in phase 4.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET082+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET082+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
%
%------------------------------------------------------------------------------